Absolute Value Equations Word Problems

Math 3 Absolute Value Word Problems Lesson

EQ: Can you model a real application problem

using an absolute value inequality?

Multiple Choice

What's a way to define absolute value?

• The value of a number

• The opposite of a number

• The distance of a number from zero

• The multiplicative inverse of a number

​How to set up the inequality:

​The best way to describe the absolute value word problem inequality is to describe the DISTANCE the margin of error can be FROM the target amount.

Multiple Choice

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.

• $$\left|x-0.03\right|\le20$$  

• $$\left|x-20\right|\le0.03$$  

• $$\left|x+20\right|\le0.03$$  

• $$\left|x-20\right|\ge0.03$$  

Multiple Choice

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

Multiple Choice

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| ≤ 0.5

• |W - 0.5| ≤ 25

• |W - 25| ≥ 0.5

• |W - 0.5| ≥ 25