Assignment: Solve Absolute Value Inequalities
Choose any three (3) of the following five problems to solve.
1. The average hourly wage for part-time workers at a juice bar is $9.50. The actual hourly
wage could differ from the average by as much as $1.50.
a. Write an absolute value inequality to represent this situation, using x to represent the
actual hourly wage.
|x - 9.5| ≤ 1.5
b. Solve the inequality. Show all work leading to your answer.
c.
x - 9.5 ≤ 1.5
x - 9.5 + 9.5 ≤ 1.5 + 9.5
x ≤ 11
Graph the solution on the number line. Be sure to include number labels to show the
values
x on the number line.
x - 9.5 ≥of-1.5
x - 9.5 + 9.5 ≥ -1.5 + 9.5
x≥8
8 ≤ x ≤ 11
d. Write 1-2 sentences to explain what the solution to the inequality represents for this
situation.
The actual hourly wage of a part-time worker at a juice bar can be as little as $8.00 or as
much as $11.00.
2. A candy company places an average of 20 truffles in a one-pound box. The number of truffles
per box never varies from the average by more than 2.
a. Write an absolute value inequality to represent this situation, using x to represent the
actual number of truffles per box.
|x - 20| ≤ 2
b. Solve the inequality. Show all work leading to your answer.
x - 20 ≤ 2
x - 20 + 20 ≤ 2 + 20
x ≤ 22
x - 20 ≥ -2
x - 20 + 20 ≥ -2 + 20
x ≥ 18
18 ≤ x ≤ 22
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c.
Graph the solution on the number line. Be sure to include number labels to show the
values of x on the number line.
d. Write 1-2 sentences to explain what the solution to the inequality represents for this
situation.
The actual number of truffles in a one-pound box can be as little as 18 or as much as 22.
3. For the past several months, Shawn’s time to run a mile has averaged 8.5 minutes. Her time
never varies from the average by more than 1.25 minutes.
a. Write an absolute value inequality to represent this situation, using x to represent
Shawn’s actual time to run a mile.
|x - 8.5| ≤ 1.25
b. Solve the inequality. Show all work leading to your answer.
x - 8.5 ≤ 1.25
x - 8.5 + 8.5 ≤ 1.25 + 8.5
x ≤ 9.75
c.
Graph the solution on the number line. Be sure to include number labels to show the
x - 8.5 ≥of-1.25
values
x on the number line.
x - 8.5 + 8.5 ≥ -1.25 + 8.5
x ≥ 7.25
7.25 ≤ x ≤ 9.75
d. Write 1-2 sentences to explain what the solution to the inequality represents for this
situation.
The actual amount of time it takes for Shawn to run a mile can be as little as 7.25
minutes or as much as 9.75 minutes.
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4. A musical accessory supply company manufactures a guitar string with an average diameter
of 0.026 inches. The actual diameter never varies by more than 0.002 inches.
a. Write an absolute value inequality to represent this situation, using x to represent the
actual diameter of the guitar string.
b. Solve the inequality. Show all work leading to your answer.
c.
Graph the solution on the number line. Be sure to include number labels to show the
values of x on the number line.
d. Write 1-2 sentences to explain what the solution to the inequality represents for this
situation.
5. A top-selling perfume is available in a 1.7 fluid ounce spray bottle. As long as the volume of
perfume in this bottle size never varies by more than 0.03 fluid ounces, the manufacturer is
allowed to label the bottle as containing 1.7 fluid ounces.
a. Write an absolute value inequality to represent this situation, using x to represent the
actual volume of perfume in the spray bottle.
b. Solve the inequality. Show all work leading to your answer.
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c.
Graph the solution on the number line. Be sure to include number labels to show the
values of x on the number line.
d. Write 1-2 sentences to explain what the solution to the inequality represents for this
situation.
© K12 Inc.