1. Equations & Inequalities

Linear Inequalities

1. Equations & Inequalities

Linear Inequalities

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Linear Inequalities with Fractions & Variables on Both Sides

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Union and intersection of intervals

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Definition and Technique For Solving Linear Inequalities

Solving Inequalities with No Solution or Infinite Solutions

Solving inequalities with no solution or all real numbers as solutions

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Solving A Compound Linear Inequality

Absolute Value Inequalities - How to Solve

Mario's Math Tutoring

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Showing 9 of 9 videos

Practice this topic

Multiple Choice

Express the given set in interval notation and graph.

{ $x$ | 14 ≤ $x$ < 26}

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Multiple Choice

Express the given interval in set builder notation and graph. (−∞, 0]

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Multiple Choice

Express the given set in interval notation and graph.

${$ $x$ $∣$ $x is less than or equal to 7$ $}$

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Multiple Choice

Solve the inequality. Express the solution set in interval notation and graph. $2x+12>19$

Solve the inequality. Express the solution set in interval notation and graph.

$\frac13\left(x+1\right)\ge\frac15\left(3+2x\right)$

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | = 7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x<-6

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (1, 6]

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | = -7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x≤6

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. -2

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 5, 2)

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > -7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x^2≥0

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II . x≥-6

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | < 7

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 3, 1]

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Textbook Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. 6≤x

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≥ 7

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≤ 7

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (2, ∞)

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≠ 7

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 3, ∞)

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ∞, 3)

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Textbook Question

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ∞, 5.5)

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- 3, 0) ∩ [- 1, 2]

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- 3, 0) ⋃ [- 1, 2]

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 3(x+5)+1≥5+3x

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- ∞, 5) ∩ [1, 8)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 8x-3x+2<2(x+7)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 2-4x+5(x-1)<-6(x-2)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (4x+7)/-3≤2x+5

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Textbook Question

In Exercises 15–26, use graphs to find each set. (- ∞, 5) ⋃ [1, 8)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (2x-5)/-8≤1-x

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. (1/3)x+(2/5)x-(1/2)(x+3)≤1/10

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Textbook Question

In Exercises 15–26, use graphs to find each set. [3, ∞) ∩ (6, ∞)

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. -(2/3)x-(1/6)x+(2/3)(x+1)≤4/3

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Textbook Question

In Exercises 15–26, use graphs to find each set. [3, ∞) ⋃ (6, ∞)

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Textbook Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 5x + 11 < 26

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 3x - 4 | < 2

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Example 4. -5<5+2x<11

Solve each inequality. Give the solution set in interval notation. . | 3x - 4 | ≥ 2

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 1/2 - x | ≤ 2

Solve each inequality. Give the solution set in interval notation. See Example 4. 10≤2x+4≤16

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 3/5 + x | < 1

Solve each inequality. Give the solution set in interval notation. See Example 4. 2>-6x+3>-3

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Textbook Question

Solve each inequality. Give the solution set in interval notation. 5| x + 1 | > 10

Solve each inequality. Give the solution set in interval notation. See Example 4. -4≤(x+1)/2≤5

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 5 - 3x | > 7

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 7 - 3x | > 4

Solve each inequality. Give the solution set in interval notation. | 5 - 3x | ≤ 7

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Textbook Question

Solve each inequality. Give the solution set in interval notation. See Example 4. 1≤(4x-5)/2<9

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 7 - 3x | ≤ 4

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | (2/3)x + 1/2 | ≤ 1/6

Solve each inequality. Give the solution set in interval notation. | 5/3 - (1/2) x | > 2/9

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Textbook Question

Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

Explain why the equation | x | = √x² has infinitely many solutions.

Solve each equation or inequality. |4x + 3| - 2 = -1

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Textbook Question

Solve each equation or inequality. |8 - 3x| - 3 = -2

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Textbook Question

Solve each equation or inequality. |6 - 2x | + 1 = 3

Solve each equation or inequality. | 4 - 4x | + 2 = 4

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Textbook Question

Solve each equation or inequality. | 3x + 1 | - 1 < 2

Solve each equation or inequality. | 5x + 2 | - 2 < 3

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Textbook Question

Solve each equation or inequality. | 5x + 1/2 | -2 < 5

Solve each equation or inequality. | 2x+ 1/3 | +1 < 4

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Textbook Question

Solve each equation or inequality. | 10 - 4x | + 1 ≥ 5

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Textbook Question

In Exercises 51–58, solve each compound inequality. 6 < x + 3 < 8

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Textbook Question

Solve each equation or inequality. | 12- 5x | + 3 ≥ 9

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Textbook Question

In Exercises 51–58, solve each compound inequality. - 3 ≤ x - 2 < 1

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Textbook Question

Solve each equation or inequality. | 3x- 7 | + 1 < -2

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Textbook Question

Solve each equation or inequality. |-5x + 7 | - 4 < -6

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Textbook Question

In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5

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Textbook Question

Solve each equation or inequality. | 10- 4x | ≥ 4

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Textbook Question

Solve each equation or inequality. | 12- 9x | ≥ -12

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Textbook Question

Solve each equation or inequality. | 6- 3x | 4 < -11

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Textbook Question

In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3)x - 5 < - 1

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Textbook Question

Solve each equation or inequality. |18- 3x | 4 < -13

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x| < 3

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Textbook Question

Solve each equation or inequality. | 8x + 5| = 0

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Textbook Question

Solve each equation or inequality. | 7 + 2x| = 0

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Textbook Question

Solve each equation or inequality. | 4.3x + 9.8| < 0

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x - 1| ≤ 2

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Textbook Question

Solve each equation or inequality. | 1.5x - 14| < 0

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x + 3| ≤ 4

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |2x - 6| < 8

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3x + 5| < 17

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |2(x - 1) + 4| ≤ 8

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Textbook Question

Solve each equation or inequality. | 4x+ 3| > 0

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3(x - 1)/4| < 6

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Textbook Question

Write each statement using an absolute value equation or inequality. . m is no more than 2 units from 7.

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x| > 3

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |x - 1| ≥ 2

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7

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Textbook Question

Write each statement using an absolute value equation or inequality. r is no less than 1 unit from 29.

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Textbook Question

Write each statement using an absolute value equation or inequality. q is no more than 8 units from 22.

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |(2x + 2)/4| ≥ 2

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3 - (2/3)x| > 5

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Textbook Question

The temperatures on the surface of Mars in degrees Celsius approximately satisfy the inequality |C + 84 | ≤ 6. What range of temperatures corresponds to this inequality?

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 3|x - 1| + 2 ≥ 8

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 5|2x + 1| - 3 ≥ 9

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. - 2|x - 4| ≥ - 4

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. - 4|1 - x| < - 16

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Textbook Question

To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x^2 - x | = 6, work Exercises 83–86 in order. For x^2 - x to have an absolute value equal to 6, what are the two possible values that x may assume? (Hint: One is positive and the other is negative.)

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 11x≥2(x-4)

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 3 ≤ |2x - 1|

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Textbook Question

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 7x-2(x-3) ≤5(2-x)

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Textbook Question

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | 3x^2 + x | = 14

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 5 ≤ 2x -3 ≤ 7

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 5 > |4 - x|

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Textbook Question

Solve each inequality. Give the solution set using interval notation. -8 >3x-5>-12

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 1 < |2 - 3x|

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 12 < |- 2x + 6/7| + 3/7

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Textbook Question

In Exercises 59–94, solve each absolute value inequality. 4 + |3 - x/3| ≥ 9

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y1 = x/2 + 3, y2 = x/3 + 5/2, and y1 ≤ y2

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y1 = (2/3)(6x - 9) + 4, y2 = 5x + 1, and y1 > y2

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = 2x - 11 + 3(x + 2) and y is at most 0

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = |2x - 5| + 1 and y > 9

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Textbook Question

Solve and graph the solution set on a number line: 3|2x-1| ≥ 21

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Textbook Question

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. y = 8 - |5x + 3| and y is at least 6

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Textbook Question

In Exercises 103–104, use the graph of y = |4 - x| to solve each inequality.

In Exercises 105–106, use the table to solve each inequality. - 3 < 2x - 5 ≤ 3

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Textbook Question

When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. Use interval notation to express the set of all numbers that satisfy this condition.

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Textbook Question

When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval notation to express the set of all numbers that satisfy this condition.

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Textbook Question

Solve and graph the solution set on a number line: (2x−3)/4 ≥ 3x/4 + 1/2

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Textbook Question

Solve each equation or inequality. |8-5x| ≥ 2

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Textbook Question

Solve each equation or inequality. |7x-3| > 4

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Textbook Question

Solve each equation or inequality. |7x+8| - 6 > -3

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Textbook Question

Solve each equation or inequality. |4x-12| ≥ -3

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Textbook Question

Write each statement using an absolute value equation or inequality. p is at least 3 units from 1.

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Textbook Question

Solve each problem. Suppose two acid solutions are mixed. One is 26% acid and the other is 34% acid. Which one of the following concentrations cannot possibly be the concentration of the mixture? A. 24% B. 30% C. 31% D. 33%

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Textbook Question

In Exercises 107–110, use graphs to find each set. [1,3) ∩ (0,4)

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Textbook Question

In Exercises 107–110, use graphs to find each set. (-2,1] ∩ [-1,3)

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Textbook Question

In Exercises 104–106, express each interval in set-builder notation and graph the interval on a number line. (-2, ∞)

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Textbook Question

In Exercises 61–64, find the domain of each function. f(x) = √(x/(2x - 1) - 1)

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Textbook Question

In Exercises 61–64, find the domain of each function. f(x) = √(2x/(x + 1) - 1)

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Textbook Question

In Exercises 61–64, find the domain of each function. f(x) = 1/√(4x^2 - 9x + 2)

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Textbook Question

In Exercises 61–64, find the domain of each function. f(x) = √(2x^2 - 5x + 2)

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^3≤4x^2

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^3≥9x^2

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^3+x^2+4x+4>0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^3−3x^2−9x+27<0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^3+2x^2−4x−8≥0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^3+2x^2−x−2≥0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (2−x)^2(x−7/2)<0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (1−x)^2(x−5/2)<0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x(4−x)(x−6)≤0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x(3−x)(x−5)≤0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x+1)(x+2)(x+3)≥0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x−1)(x−2)(x−3)≥0

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. x/(x−3)>0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 4x^2−4x+1≥0

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (3x+5)/(6−2x)≥0

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (4−2x)/(3x+4)≤0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 9x^2−6x+1<0

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (−x−3)/(x+2)≤0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2≤2x+2

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (−x+2)/(x−4)≥0

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x+3)/(x+4)<0

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x−4)/(x+3) > 0

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Textbook Question

Solve each inequality in Exercises 86–91 using a graphing utility. 1/(x + 1) ≤ 2/(x + 4)

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2≤4x−2

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Textbook Question

Solve each inequality in Exercises 86–91 using a graphing utility. (x - 4)/(x - 1) ≤ 0

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Textbook Question

Solve each inequality in Exercises 86–91 using a graphing utility. x^3 + x^2 - 4x - 4 > 0

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Textbook Question

Solve each inequality in Exercises 86–91 using a graphing utility. 2x^2 + 5x - 3 ≤ 0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. −x^2+2x≥0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. −x^2+x≥0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x^2−5x≤0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 2x^2+3x>0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2+2x<0

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Textbook Question

Solve each inequality in Exercises 86–91 using a graphing utility. x^2 + 3x - 10 > 0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2−4x≥0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 4x^2+1≥4x

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 5x≤2−3x^2

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Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x^2+16x<−5

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Textbook Question

In Exercises 69–74, solve each inequality and graph the solution set on a real number line. (x + 3)/(x - 4) ≤ 5

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Textbook Question

In Exercises 69–74, solve each inequality and graph the solution set on a real number line. 2x^2 + 9x + 4 ≥ 0

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Textbook Question

In Exercises 69–74, solve each inequality and graph the solution set on a real number line. 2x^2 + 5x - 3 < 0

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Textbook Question

Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. x^2 - x - 6 < 0

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Textbook Question

Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. x^2 - 9x + 20 < 0

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Textbook Question

Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. 2x^2 - 9x ≥ 18

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Textbook Question

Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. 3x^2 + x ≥ 4

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Textbook Question

Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. -x^2 + 4x + 1 ≥ 0

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Textbook Question

Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. -x^2 + 2x + 6 > 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) = 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) < 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) > 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) ≥ 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} = 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} < 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} > 0

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Textbook Question

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} ≤ 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (2x - 1)(5x - 9)(x - 4) < 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (x - 4)(2x + 3)(3x - 1) ≥ 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (x - 3)(x - 4)(x - 5)^2 ≤ 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. -(x - 3)(x - 4)^2 (x - 5) > 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (x + 3)^3(2x - 1)(x + 4) ≥ 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. 2x^3 - 7x^2 ≥ 3 - 8x

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. x^4 - x^3 - 10x^2 - 8x < 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. x^4 + 2x^3 + 36 < 11x^2 + 12x

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. (x - 1)/(x - 4) > 0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. (x + 1)/(x - 5) > 0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. (2x + 3)/(x - 5) ≤ 0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. (3x + 7)/(x - 3) ≤ 0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 8 /(x - 2) ≥ 2

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 20/(x - 1) ≥ 1

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. (x - 8)/(x - 4) < 3

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. (2x - 3)/(x + 1) > 4

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (a) (x - 5)(x + 2) ≥ 0 (b) (x - 5)(x + 2) > 0 (c) (x - 5)(x + 2) ≤ 0 (d) (x - 5)(x + 2) < 0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (a) -(x + 1)(x + 2) ≥ 0 (b) -(x + 1)(x + 2) > 0 (c) -(x + 1)(x + 2) ≤ 0 (d) -(x + 1)(x + 2) < 0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. - ( x +√2)(x-3) < 0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (x-4)(x + √2) < 0

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. x^5 + x^2 + 2 ≥ x^4 + x^3 + 2x

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. x^4 + 6x^2 + 1 ≥ 4x^3 + 4x

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (x - 4)^2 ≤ 0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. -(x + 1)^2 ≥ 0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. x^2 + x - 30 ≤ 0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. x^2 - 2 > x

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. 2^x2 + 5 ≤ 11x

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Textbook Question

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. 23. (a) -x(x - 1)(x - 2) ≥ 0 (b) -x(x - 1)(x - 2) > 0 (c) -x(x - 1)(x - 2) ≤ 0 (d) -x(x - 1)(x - 2) < 0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. {x^2 - 3x- 4} /{ x^2 + 6x + 9} ≤ 0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 1 /{x+ 2} > 1 /{ x -3}

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 1 /{x - 1} < 1 /{ x + 1}

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 2 /{x - 2} ≥ 1 / x

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 5 /{x + 3} ≥ 3 /x

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 5 /{2 - x} > 3 /{ 3 - x}

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 3 /{4 - x} > 6 /{ 1 - x}

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 1 /{x^2 - 4} ≤ 1 /{ 2 - x}

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 1 /{x^2 - 4x + 3} ≤ 1 /{ 3 - x}

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Textbook Question

Solve each inequality. Give the solution set in interval notation. (2x-1)(x+5)<0

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Textbook Question

Solve each inequality. Give the solution set in interval notation. (x-4)(x-1)(x+2)>0

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Textbook Question

Solve each inequality. Give the solution set in interval notation. (x+7)/(2x+1)<0

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Textbook Question

Solve each inequality. Give the solution set in interval notation. 4/(x+6)>2/(x-1)

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Textbook Question

Fill in the blank(s) to correctly complete each sentence. A polynomial function with leading term 3x^5 has degree ____.

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (2x-3)/x^2+1≥0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (9x-8)/(4x^2+25)<0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (5-3x)^2/(2x-5)^3>0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (5x-3)^3/(25-8x)^2≤0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (2x-3)(3x+8)/(x-6)^3≥0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (9x-11)(2x+7)/(3x-8)^3>0

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Textbook Question

Solve each problem. See Example 7. A baseball is hit so that its height, s, in feet after t seconds is s=-16t^2+44t+4. For what time period is the ball at least 32 ft above the ground?

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Textbook Question

Solve each problem. See Example 7. Velocity of an Object The velocity of an object, v, after t seconds is given by v=3t^2-18t+24.Find the interval where the velocity is negative.

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Textbook Question

Answer the following. Why can 3 not be in the solution set of 14x+9 / x-3 < 0? (Do not solve the inequality.)

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Textbook Question

Answer the following. Why must -4 be in the solution set of x+4 / 2x+1 ≥ 0? (Do not solve the inequality.)

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2-7x+10<0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2-x-6>0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2-7x+10>0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. 2x^2-9x≤18

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. 3x^2+x≤4

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x(x-1)≤6

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x(x+1)<12

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2≤9

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2>16

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Textbook Question

Which inequality has solution set (-∞, ∞)? A. (x-3)^2≥0 B. (5x-6)^2≤0 C. (6x+4)^2>0 D. (8x+7)^2<0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 1/(x+2)≥3

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 7/(x+2)≥1/(x+2)

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 5/(x+1)>12/(x+1)

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 5/(1-x)≤2/(1-x)

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 4/(3+x)≤3/(3+x)

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 3/(2x-1)>-4/x

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 4/(2-x)≥3/(1-x)

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 4/(x+1)<2/(x+3)

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x+3)/(2x-5)≤1

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x+2)/(2x+3)≤5

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Textbook Question

Solve each inequality. Give the solution set using interval notation. x²-3x ≥ 5

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 3x+6 / x-5 > 0

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Textbook Question

Solve each inequality. Give the solution set using interval notation. x+7 / 2x+1 ≤1

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 3x-2/x - 4 > 0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. 4x^2+3x+1≤0

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2-2x≤1

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Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2+4x>-1

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x-3)/(x+5)≤0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x-1)/(x-6)≤0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x+2)/(x+7)≥0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x+1)/(x-4)>0

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (1-x)/(x+2)>-1

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (6-x)/(x+2)>1

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 3/(x-6)≤2

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 3/(x-2)<1

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. -4/(1-x)<5

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 10/(x+3)≥1

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 3/(x+5)>2

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Textbook Question

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 10/(3+2x)≤5

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 5x+2/x +1 < 0

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 3/x-1 ≤ 5/x+3

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Textbook Question

Solve each inequality. Give the solution set using interval notation. 3/x+2 > 2/x-4

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x−4)(x+2)>0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x+3)(x−5)>0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x+1)(x−7)≤0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2+5x+4>0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2−6x+9<0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x^2+10x−8≤0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 9x^2+3x−2≥0

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 2x^2+x<15

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Textbook Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 6x^2+x>1

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x+4)/x>0

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x+4)(x−1)/(x+2)≤0

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Textbook Question

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. |x^2 + 2x - 36| > 12

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Textbook Question

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. 3/(x +3) > 3/(x - 2)

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Textbook Question

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. 1/(x + 1) > 2/(x - 1)

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Textbook Question

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. (x^2 -x - 2)/(x^2 - 4x + 3) > 0

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Textbook Question

In Exercises 71–72, use the graph of the polynomial function to solve each inequality.

2x^3 + 11x^2 ≥ 7x + 6

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Textbook Question

In Exercises 71–72, use the graph of the polynomial function to solve each inequality.

2x^3 + 11x^2 < 7x + 6

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Textbook Question

In Exercises 73–74, use the graph of the rational function to solve each inequality.

1/4(x + 2) ≤ - 3/4(x - 2)

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Textbook Question

In Exercises 73–74, use the graph of the rational function to solve each inequality.

1/4(x + 2) > - 3/4(x - 2)

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x - 2)/(x + 2) ≤ 2

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. x/(x + 2) ≥ 2

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x + 1)/(x + 3) < 2

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x + 4)/(2x - 1) ≤ 3

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Textbook Question

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation.1/(x - 3) < 1

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