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Table of contents

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0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

2:49 minutes

Problem 17bLial - 13th Edition

Textbook Question

Solve each equation. 3x+5 - 5(x+1)= 6x+7

Verified step by step guidance

1

Distribute the -5 across the terms inside the parentheses:

- 5 (x + 1) = - 5 x - 5

.

Rewrite the equation with the distributed terms:

3 x + 5 - 5 x - 5 = 6 x + 7

.

Combine like terms on the left side:

3 x - 5 x + 5 - 5 = - 2 x

.

The equation now is

- 2 x = 6 x + 7

.

Move all terms involving

x

to one side by adding

2 x

to both sides:

0 = 8 x + 7

.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside parentheses. In the given equation, applying the distributive property to -5(x + 1) is essential to simplify the expression correctly.

Recommended video:

Multiply Polynomials Using the Distributive Property

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is crucial in simplifying equations, as it helps to consolidate terms and make the equation easier to solve. In the equation provided, combining like terms will help isolate the variable x.

Recommended video:

Combinations

Isolating the Variable

Isolating the variable means rearranging the equation to get the variable on one side and the constants on the other. This process often involves performing inverse operations, such as addition or subtraction, and is key to solving for the variable. In the context of the equation, isolating x will lead to the final solution.

Recommended video:

Equations with Two Variables

Watch next

Master Introduction to Solving Linear Equtions with a bite sized video explanation from Callie

Related Videos

Related Practice

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1/x + 2 = 3/x

Textbook Question

In Exercises 1–26, solve and check each linear equation. 4x + 9 = 33

Textbook Question

Solve each equation. 2x+8 = 3x+2

Textbook Question

Solve each equation. 5x-2(x+4)=3(2x+1)

Textbook Question

In Exercises 1–26, solve and check each linear equation. 7x - 5 = 72

Textbook Question

Solve each equation. A= 24f / B(p+1), for f (approximate annual interest rate)

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (x−2)/2x + 1 = (x+1)/x

Textbook Question

Decide whether each statement is true or false. The solution set of 2x+5=x -3 is {-8}.

Textbook Question

Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.) A. 5x+3 =11 B.12x+6 =-4 C.100x =50(x+3) D. 6(x+4) =x+24

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 3/(x+1) = 5/(x−1)

Textbook Question

In Exercises 1–26, solve and check each linear equation. 11x - (6x - 5) = 40

Textbook Question

Decide whether each statement is true or false. The equation 5x=4x is an example of a contradiction.

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (x−6)/(x+5) = (x−3)/(x+1)

Textbook Question

In Exercises 1–26, solve and check each linear equation. x - 5(x + 3) = 13

Textbook Question

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 3x/4 - x/3 + 1 = 4x/5 - 3/20

Textbook Question

Solve each equation. 5x+4= 3x-4

Textbook Question

In Exercises 1–26, solve and check each linear equation. 2x - 7 = 6 + x

Textbook Question

Solve each equation. 6(3x-1)= 8 - (10x-14)

Textbook Question

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 4x-2(1-x)=3(2x+1)-5

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1 − 4/(x+7) = 5/(x+7)

Textbook Question

In Exercises 1–26, solve and check each linear equation. 7x + 4 = x + 16

Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7

Textbook Question

In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x

Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2

Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2(x-4)+3(x+5)=2x-2

Textbook Question

Solve each equation. 4[2x-(3-x)+5] = -6x - 28

Textbook Question

In Exercises 1–26, solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 6/x − x/3 = 1

Textbook Question

Solve each equation. 1/15(2x+5) = 1/9(x+2)

Textbook Question

In Exercises 1–26, solve and check each linear equation. 2 - (7x + 5) = 13 - 3x

Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7x + 13 = 2(2x-5) + 3x + 23

Textbook Question

Solve each equation. 0.2x - 0.5 = 0.1x+7

Textbook Question

In Exercises 1–26, solve and check each linear equation. 16 = 3(x - 1) - (x - 7)

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1/x−1 + 1/x+1 = 2/x²−1

Textbook Question

Solve each equation. 0.5x+ 4/3x= x+10

Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. (3x+1)/3 - 13/2 = (1-x)/4

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/3 = x/2 - 2

Textbook Question

In Exercises 25-38, solve each equation. 20 - x/3=x/2

Textbook Question

Solve each equation. 0.08x+0.06(x+12) = 7.72

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 2/(x+3) − 5/(x+1) = (3x+5)/(x²+4x+3)

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1

Textbook Question

Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 1/2(6x+20) = x+4 +2(x+3)

Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 3y/(y²+5y+6) + 2/(y²+y−2) = 5y/(y²+2y−3)

Textbook Question

In Exercises 25-38, solve each equation. (x + 3)/6 = 2/3 + (x - 5)/4

Textbook Question

Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 2(x-8) = 3x-16

Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0

Textbook Question

In Exercises 25-38, solve each equation. x/4 =2 +(x-3)/3

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8

Textbook Question

Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. -0.6(x-5)+0.8(x-6) = 0.2x - 1.8

Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. I=Prt,for P (simple interest)

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 4/x = 5/2x + 3

Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. P=2l+2w,for w (perimeter of a rectangle)

Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. F = GMm/r², for m (force of gravity)

Textbook Question

Solve and check: 24 + 3 (x + 2) = 5(x − 12).

Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. s = 1/2gt², for g (distance traveled by a falling object)

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 5/2x - 8/9 = 1/18 - 1/3x

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. (x - 2)/2x + 1 = (x + 1)/x

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 1/(x - 1) + 5 = 11/(x - 1)

Textbook Question

Solve each equation for x. 2(x-a) +b =3x+a

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)

Textbook Question

Solve each equation for x. ax+b=3(x-a)

Textbook Question

Solve each equation for x. x/a-1 = ax+3

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(2x - 2) + 1/2 = 2/(x - 1)

Textbook Question

Solve each equation for x. a²x + 3x =2a²

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 2) + 2/(x - 2) = 8/(x + 2)(x - 2)

Textbook Question

Solve: 2x(x+3)+6(x−3)=−28. (Section 5.7, Example 2)

Textbook Question

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.

Textbook Question

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (x - 3)/5, y2 = (x - 5)/4, and y1 - y2 = 1.

Textbook Question

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (2x - 1)/(x^2 + 2x - 8), y2 = 2/(x + 4), y3 = 1/(x - 2), and y1 + y2 = y3.

Textbook Question

In Exercises 67–70, find all values of x such that y = 0. y = 2[3x - (4x - 6)] - 5(x - 6)

Textbook Question

In Exercises 67–70, find all values of x such that y = 0. y = (x + 6)/(3x - 12) - 5/(x - 4) - 2/3

Textbook Question

In Exercises 67–70, find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5

Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x + 7 = 7(x + 1) - 3x

Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x

Textbook Question

Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8

Textbook Question

Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).

Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3

Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7

Textbook Question

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)

Textbook Question

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x/(x + 3) - 12/(x - 3) = (4x^2 + 36)/(x^2 - 9)

Textbook Question

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x^2 + 3x - 10) - 1/(x^2 + x - 6) = 3/(x^2 - x - 12)

Textbook Question

Retaining the Concepts. Solve and determine whether 8(x - 3) + 4 = 8x - 21 is an identity, a conditional equation, or an inconsistent equation.

Textbook Question

Evaluate x^2 - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).

Textbook Question

In Exercises 99–106, solve each equation. [(3 + 6)^2 ÷ 3] × 4 = - 54 x

Textbook Question

In Exercises 99–106, solve each equation. 5 - 12x = 8 - 7x - [6 ÷ 3(2 + 5^3) + 5x]

Textbook Question

In Exercises 99–106, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)

Textbook Question

In Exercises 99–106, solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)

Textbook Question

Solve: 9(x − 1) = 1 + 3(x−2). (Section 1.4, Example 3)

Textbook Question

What is an identity equation? Give an example.

Textbook Question

What is a conditional equation? Give an example.

Textbook Question

What is an inconsistent equation? Give an example.

Textbook Question

Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.

Textbook Question

After a 30% price reduction, you purchase a 50″ 4K UHD TV for $245. What was the television's price before the reduction?

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = 2lw + 2lh + 2wh for h

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = C/(1 - r) for r

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = P + Prt for r

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? E = mc^2 for m

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? V = (1/3)Bh for B

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = (1/2)bh for b

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? D = RT for R

Textbook Question

A job pays an annual salary of $57,900, which includes a holiday bonus of $1500. If paychecks are issued twice a month, what is the gross amount for each paycheck?

Textbook Question

For an international telephone call, a telephone company charges $0.43 for the first minute, $0.32 for each additional minute, and a $2.10 service charge. If the cost of a call is $5.73, how long did the person talk?

Textbook Question

A repair bill on a sailboat came to $2356, including $826 for parts and the remainder for labor. If the cost of labor is $90 per hour, how many hours of labor did it take to repair the sailboat?

Textbook Question

An automobile repair shop charged a customer $1182, listing $357 for parts and the remainder for labor. If the cost of labor is $75 per hour, how many hours of labor did it take to repair the car?

Textbook Question

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

Textbook Question

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

Textbook Question

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

Textbook Question

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

Textbook Question

Exercises 19–20 involve markup, the amount added to the dealer's cost of an item to arrive at the selling price of that item. The selling price of a refrigerator is $1198. If the markup is 25% of the dealer's cost, what is the dealer's cost of the refrigerator?

Textbook Question

Including a 17.4% hotel tax, your room in Chicago cost $287.63 per night. Find the nightly cost before the tax was added.

Textbook Question

Including a 10.5% hotel tax, your room in San Diego cost $216.58 per night. Find the nightly cost before the tax was added.

Textbook Question

After a 20% reduction, you purchase a television for $336. What was the television's price before the reduction?

Textbook Question

An electronic pass for a toll road costs $30. The toll is normally $5.00 but is reduced by 30% for people who have purchased the electronic pass. Determine the number of times the road must be used so that the total cost without the pass is the same as the total cost with the pass.

Textbook Question

You are choosing between two gyms. One gym offers membership for a fee of $40 plus a monthly fee of $25. The other offers membership for a fee of $15 plus a monthly fee of $30. After how many months will the total cost at each gym be the same? What will be the total cost for each gym?

Textbook Question

Exercises 141–143 will help you prepare for the material covered in the next section. If the width of a rectangle is represented by x and the length is represented by x + 200, write a simplified algebraic expression that models the rectangle's perimeter.

Textbook Question

In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

Textbook Question

In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g

Textbook Question

In Exercises 36–43, use the five-step strategy for solving word problems. The length of a rectangular field is 6 yards less than triple the width. If the perimeter of the field is 340 yards, what are its dimensions?

Textbook Question

In Exercises 36–43, use the five-step strategy for solving word problems. An apartment complex has offered you a move-in special of 30% off the first month's rent. If you pay $945 for the first month, what should you expect to pay for the second month when you must pay full price?

Textbook Question

Work each problem. Elmer borrowed $3150 from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4%. (a)How much will the interest amount to?

Textbook Question

Work each problem. Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%. (a)How much must she pay the bank in 18 months?

Textbook Question

Solve each problem. How long will it take a car to travel 400 mi at an average rate of 50 mph?

Textbook Question

Solve each problem. If a train travels at 80 mph for 15 min, what is the distance traveled?

Textbook Question

Solve each problem. If a person invests $500 at 2% simple interest for 4 yr, how much interest is earned?

Textbook Question

Solve each problem. If 120 L of an acid solution is 75% acid, how much pure acid is there in the mixture?

Textbook Question

Solve each problem. Which one or more of the following cannot be a correct equation to solve a geometry problem, if x represents the length of a rectangle? (Hint: Solve each equation and consider the solution.) A. 2x+2(x- ) = 14 B. -2x+7(5-x) = 52 C. 5(x+2)+5x = 10 D. 2x+2(x-3) = 22

Textbook Question

Solve each problem. See Example 1. Michael must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be 44 ft. Find the length and the width of the shed.

Textbook Question

Solve each problem. See Example 1. The length of a rectangular label is 2.5 cm less than twice the width. The perimeter is 40.6 cm. Find the width. (Side lengths in the figure are in centimeters.)

Textbook Question

Solve each problem. See Example 1. The perimeter of a triangular plot of land is 2400 ft.The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot.

Textbook Question

Solve each problem. See Example 2. Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr?

Textbook Question

Solve each problem. See Example 4. In planning her retirement, Kaya deposits some money at 2.5% interest, and twice as much money at 3%. Find the amount deposited at each rate if the total annual interest income is $850.

Textbook Question

Solve each problem. See Example 4. Zhu inherited $200,000 from her grandmother. She first gave 30% to her favorite charity. She invested some of the rest at 1.5% and some at 4%, earning $4350 interest per year. How much did she invest at each rate?

Textbook Question

Solve each problem. See Examples 5 and 6. Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot (μg/ft^3), eye irritation can occur. One square foot of new plywood could emit 140 μg per hr. (Data from A. Hines, Indoor Air Quality & Control.) A room has 100 ft^2 of new plywood flooring. Find a linear equation F that computes the amount of formaldehyde, in micrograms, emitted in x hours.

Textbook Question

Solve each problem. See Examples 5 and 6. Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot (μg/ft^3), eye irritation can occur. One square foot of new plywood could emit 140 μg per hr. (Data from A. Hines, Indoor Air Quality & Control.) The room contains 800 ft^3 of air and has no ventilation. Determine how long it would take for concentrations to reach 33 μg/ft^3. (Round to the nearest tenth.)

Textbook Question

Solve each problem. Dimensions of a Square. If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original square?

Textbook Question

Solve each problem. Speed of a PlaneMary Lynn left by plane to visit her mother in Louisiana, 420 km away. Fifteen minutes later, her mother left to meet her at the airport. She drove the 20 km to the airport at 40 km per hr, arriving just as the plane taxied in. What was the speed of the plane?

Textbook Question

Solve each problem. (Modeling) Lead IntakeAs directed by the 'Safe Drinking Water Act' of December 1974, the EPA proposed a maximum lead level in public drinking water of 0.05 mg per liter. This standard assumed an individual consumption of two liters of water per day. (a)If EPA guidelines are followed, write an equation that models the maximum amount of lead A ingested in x years. Assume that there are 365.25 days in a year.

Textbook Question

Solve each problem. (Modeling) Online Retail SalesProjected retail e-commerce sales (in billions of dollars) for the years 2016–2022 can be modeled by the equation y=52.304x+396.80, where x=0 corresponds to 2016, x=1 corresponds to 2017, and so on. Based on this model, find projected retail e-commerce sales in 2022 to the nearest tenth of a billion. (Data from www.statista.com)

Textbook Question

In the metric system of weights and measures, temperature is measured in degrees Celsius (°C) instead of degrees Fahrenheit (°F). To convert between the two systems, we use the equations. C =5/9 (F-32) and F = 9/5C+32. In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. 20°C

Textbook Question

In the metric system of weights and measures, temperature is measured in degrees Celsius (°C) instead of degrees Fahrenheit (°F). To convert between the two systems, we use the equations. C =5/9 (F-32) and F = 9/5C+32. In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. 50°F

Textbook Question

Work each problem. Round to the nearest tenth of a degree if necessary. Temperature of VenusVenus is the hottest planet, with a surface temperature of 867°F. What is this temperature in degrees Celsius? (Data from The World Almanac and Book of Facts.)

Textbook Question

Work each problem. Round to the nearest tenth of a degree if necessary. Temperature in South CarolinaA record high temperature of 113°F was recorded for the state of South Carolina on June 29, 2012. What is the corresponding Celsius temperature? (Data from U.S. National Oceanic and Atmospheric Administration.)

Textbook Question

In the metric system of weights and measures, temperature is measured in degrees Celsius (°C) instead of degrees Fahrenheit (°F). To convert between the two systems, we use the equations. C =5/9 (F-32) and F = 9/5C+32. In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. 100°F

Textbook Question

Solve each problem. See Example 2. Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In 1/2 hr, the planes are 275 mi apart. What are their speeds?

Textbook Question

Solve each problem. See Example 2. In the Apple Hill Fun Run, Mary runs at 7 mph, Janet at 5 mph. If they start at the same time, how long will it be before they are 1.5 mi apart?

Textbook Question

Solve each problem. See Example 2. At the 2008 Summer Olympics in Beijing, Usain Bolt set a new Olympic and world record in the 100-m dash with a time of 9.69 sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be? How would this time compare to the fastest time for a marathon, which is 2 hr, 3 min, 23 sec, set in 2013? (Hint: 1 m ≈ 3.281 ft.) (Data from Sports Illustrated Almanac.)

Textbook Question

Solve each problem. See Example 2. Callie took 20 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 15 min. If the current in that part of the river is 5 km per hr, what was her boat speed?

Textbook Question

Solve each problem. See Example 3. How many gallons of a 5% acid solution must be mixed with 5 gal of a 10% solution to obtain a 7% solution?

Textbook Question

Solve each problem. See Example 3. Aryan wishes to strengthen a mixture from 10% alcohol to 30% alcohol. How much pure alcohol should be added to 7 L of the 10% mixture?

Textbook Question

Solve each problem. See Example 3. How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%?

Textbook Question

Solve each problem. See Example 4. Cody sells some property for $240,000. The money will be paid off in two ways: a short-term note at 2% interest and a long-term note at 2.5%. Find the amount of each note if the total annual interest paid is $5500.

Textbook Question

After a 20% reduction, a 42-inch HDTV sold for $256. What was the price before the reduction?

Textbook Question

In Exercises 137–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation |x| = - 6 is equivalent to x = 6 or x = - 6.

Textbook Question

In Exercises 91–100, find all values of x satisfying the given conditions. y = |2 - 3x| and y = 13

Textbook Question

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |4x - 3| = |4x - 5|

Textbook Question

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|4 - (5/2)x| + 6 = 18

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 7|5x| + 2 = 16

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|3x - 2| = 14

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| = 5

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x - 2| = 7

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x| = 8

Textbook Question

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 8) - √(x - 4) = 2

Textbook Question

Solve each equation in Exercises 96–102 by the method of your choice. -4|x+1| + 12 = 0

Textbook Question

Solve the equations containing absolute value in Exercises 94–95. |2x+1| = 7

Textbook Question

Solve each equation. |x + 1 | = |1 -3x|

Textbook Question

Solve each equation. |3 - 2x | = |5 - 2x |

Textbook Question

Solve each equation or inequality. |x+4| = 7

Textbook Question

Solve each equation or inequality. |7/2-3x| -9=0

Textbook Question

Solve each equation or inequality. |5x-1| = |2x+3|

Textbook Question

Solve each equation or inequality. |x+10| = |x-11|

Textbook Question

Solve each equation. |3x - 1 | = 2

Textbook Question

Solve each equation. | 4x + 2 | = 5

Textbook Question

Solve each equation. |7 - 3x| = 3

Textbook Question

Solve each equation. | x - 4/ 2| = 5

Textbook Question

Match each equation in Column I with the correct first step for solving it in Column II. √(x+5) = 7

Textbook Question

Solve each equation. See Examples 4–6. √x-√(x-12)=2

Textbook Question

Solve each equation. √x-√x+3= -1

Textbook Question

Solve each equation. See Examples 4–6. √x-√(x-5)=1

Textbook Question

Solve each equation. See Examples 4–6. √(x+5) + 2 = √(x-1)

Textbook Question

Solve each equation. See Examples 4–6. √(x+7)+3=√(x-4)

Textbook Question

Solve each equation. See Examples 4–6. ∛(4x+3)=∛(2x-1)

Textbook Question

Solve each equation. See Examples 4–6. ∛2x=∛(5x+2)

Textbook Question

Solve each equation. See Examples 4–6. ∜(x-15)=2

Textbook Question

Solve each equation. See Examples 4–6. ∜(3x+1)=1

Textbook Question

Solve each equation. See Example 7. (3x+7)^1/3-(4x+2)^1/3=0

Textbook Question

Solve each equation. √4x-2 = √3x+1

Textbook Question

Solve each equation. ⁵√ 2x = ⁵√ 3x+2

Textbook Question

Solve: 6|1 – 2x| — 7 = 11.

Multiple Choice

Solve the Equation. $3\left(2-5x\right)=4x+25$

Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. $\frac{x}{4}+\frac16=\frac{x}{3}$

Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$-2\left(5-3x\right)+x=7x-10$

Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$5x+17=8x+12-3\left(x+4\right)$

Multiple Choice

Solve the equation.

$\frac92+\frac14\left(x+2\right)=\frac34x$

Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$5 x + 17 = 8 x + 12 - 3 (x + 4)$

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