Absolute Value and Word Problems

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

• |x – 6| ≤ 0.1
• |x – 6| ≥ 0.1
• |x – 0.1| ≤ 6
• |x – 0.1| ≥ 6

The lowest test grade in a class is a 75 and the highest is 91. Write an absolute value equation that expresses the highest and lowest scores on the test

• |x+75|=91
• |x-91|=75
• |x-83|=8
• |x-8|=83

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. Which volume would NOT be included in the range of liquid?

• 19.93
• 20.013
• 20.02
• 19.99

A type of mobile phone produced by NOKIA must be less than 8 ounces in weight with a tolerance of 0.3 ounces. The mobiles that are not within the tolerated weight must be recycled. Which of the following inequalities can be used to assess which mobiles are tolerable? (W is the weight of the mobiles) .

• |w - .3| ≤ 8

• |w - .3| ≤ 8

• |w - 8| ≤.3

• |w - 8| ≤ .3

The street built in the city must be 25 feet in width with a tolerance of 0.5 feet. Streets that are not within the tolerated widths must be repaired. Which of the following inequalities can be used to assess which streets are within tolerance? (W is the width of the street) .

• |W - 25| ≤ .5
• |W - .5| ≤ 25
• |W - 25| ≥ .5
• |W - .5| ≥ 25

John is looking for a job after graduation. The salary which he is satisfied with must be $3000 with a tolerance of $500. Which of the following inequalities can be used to assess which if his salary is tolerable? (m is the measure of the salary)

• |m - 500| ≤ 3000
• |m - 500| ≥ 3000
• |m - 3000| ≥ 500
• |m - 3000| ≤ 500

John is looking for a job after graduation. The salary which he is satisfied with must be $3000 with a tolerance of $500. Choose the salary John would accept.

• $3,478
• $3,792
• $2,489
• $2,256

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. What absolute value inequality describes this situation?

• | x - 15 | ≤ 50

• | x - 50 | ≤ 15

• | x - 15 | ≥ 50

• | x - 50| ≥ 50

Which is the formula for absolute value word problems?

• |x-center|=change

• |x-change|=center

• |x-center|≤change

• |x-change|≤center

Which function is graphed?

• f(x) = 2|x + 2| -4
• f(x) = 2|x - 4| + 2
• f(x) = |x + 2| - 4
• f(x) = -2|x - 4|