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

Finding the union and intersections of intervals examples

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

Pine View Middle School Math

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3:49

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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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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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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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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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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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)

163

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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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