NEW
Font size
WorksheetsAbsolute Value Equations and Inequalities Word Problems
Total questions: 20
Worksheet time: 20mins
Save your answer to this question, you will need it for the next problem! Bottles filled in a bottling plant are advertised as being filled with 250 ml of orange juice. This is known as the spec value. The customers of this plant will tolerate volumes that differ from this spec value by up to 20 ml. Which of the following inequalities represents the volumes "V" of orange juice per bottle that will be accepted by this plant’s customers?
∣V−20∣≤250
∣V+20∣≤250
∣V−250∣≤20
∣V+250∣≤20
Save your answer to this question, you will need it for the next problem! The radius ( r ) of the gears produced at a factory must be 6 inches in length with an error tolerance of 0.1 inches. This means a gear with a radius that differs from 6 in. by more than 0.1 in. will be thrown out. Which of the following inequalities represents the values of "r" that would lead to a gear being thrown out?
∣r−6∣≤0.1
∣r−6∣>0.1
∣r−0.1∣<6
∣r−0.1∣≥6
Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.
|x - 50|=15
|x + 15|=50
|x + 50|=15
|x - 15|=50
A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.
|v - 0.03|=20
|v - 20|=0.03
|v + 0.03|=20
|v + 20|=0.03
A
B
C
D
A
B
C
D
A
B
C
D
0
-4/3 and -8/3
-4/3
{ }, no solution
a
b
c
d
| -8x | < 8
What is the correct first step?
separate into two inequalities with an "and"
separate into two inequalities with an "or"
divide both sides by -8
A
B
C
D
What is the first step in solving
|x + 4| - 8 > 2
Subtract 2 on both sides
Set up two inequalities
Divide 8 on both sides
Add 8 on both sides
The average January temperature in a northern Canadian city is 1 degree Fahrenheit. The actual January temperature for that city may be about 5 degrees warmer or colder. Write an equation to find the minimum and maximum temperatures.
|t - 1|=5
|t - 5|=1
|t + 1|=5
|t + 5|=1
Sofia is buying new skis. She finds that the average price of skis is $750 but the actual price varies by $250. Write an equation to describe this situation.
|x - 750|=250
|x - 250|=750
|x + 750|=250
|x + 250|=750
While grilling steaks, Washington likes to keep the grill temperature on 425 degrees Fahrenheit, plus or minus 15 degrees Fahrenheit. Which equation represents this situation?
|t - 425|=15
|t - 15|=425
|t + 425|=15
|t + 15|=425
Victor has a goal of making $75 per week at his after-school job. Last month he was within $6.50 of his goal. Write an equation to find the maximum and minimum amounts that Victor might have made last month?
|x - 75|=6.50
|x - 6.50|=750
|x + 75|=6.50
|x + 6.50|=75
The U.S. Mint produces quarters that weigh about 5.67 grams each. After the quarters are produced, a machine weighs them. If the quarter weighs 0.02 grams more or less than the desired weight, the quarter is rejected. Write and solve an equation to find the heaviest and lightest quarters the machine will approve.
|x - 5.67|=0.02
|x + 5.67|=0.02
|x - 0.02|=5.67
|x + 0.02|=5.67
To make cocoa powder, cocoa beans are roasted. The ideal temperatures for roasting is 300 degrees Fahrenheit, plus or minus 25 degrees Fahrenheit. Write an equation describing the maximum and minimum temperatures for cocoa beans.
|x - 300|=25
|x + 300|=25
|x - 25|=300
|x + 25|=300
A standard adult tennis racket has a 100 square-inch head, plus or minus 20 square inches. Write an equation to determine the least and greatest possible sizes for the head of an adult tennis racket.
|x - 100|=20
|x - 20|=100
|x + 100|=20
|x + 20|=100
