Absolute Value Equations

If a runner runs the first leg in 52 seconds, plus or minus 2 seconds, write an equation to find the fastest and slowest times.

• |x + 52| = 2

• |x - 52| = 2

• |x - 2| = 52

• |x + 2| = 52

The average test score was 85, plus or minus 6 points. Write an equation to represent the highest and lowest scores.

• |x + 85| = 6

• |x + 6| = 85

• |x - 85| = 6

• |x - 6| = 85

A machine is used to fill each of several bags with 16 ounces of sugar. After the bags are filled, another machine weighs them. If the bag weighs .3 ounces more or less than the desired weight, the bag is rejected. Write this equation to find the heaviest and lightest bag the machine will approve.

• |x - 16| = .3

• |x - .3| = 16

• |x + 16| = .3

• |x + .3| = 16

Leona was in a golf tournament last week. All of her four rounds of gold were within 2 strokes of par. If par was 72, write an equation to determine the maximum and minimum scores that Leona could have made in the golf tournament?

• |x - 72| = 2

• |x + 72| = 2

• |x - 2| = 72

• |x + 2| = 72

Members of the track team can run 400 m in an average time of 58.2 seconds. The fastest and slowest times varied from the average by 6.4 seconds. What were the maximum and minimum times for the track team?

• |x - 58.2| = 6.4

• |x + 58.2| = 6.4

• |x - 400| = 58.2

• |x - 6.4| = 58.2

Victor has a goal of making $75 per week at his after-school job. Last month he was within $6.50 of his goal. What are the maximum and minimum amounts that Victor might have made last month?

• |x - 75| = 6.5

• |x - 6.5| = 75

• |x + 75| = 6.5

• |x - 68.5| = 6.5

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 average temperature in Las Vegas in July is 110 degrees.  If the temperature can vary up to 10 degrees, which equation represents this situation?

• | x - 10 | < 110
• | 110 - x | < 10
• | x - 110 | < 10
• | 10 - x | < 110

The average temperature in the winter was -10 degrees, give or take 15 degrees. Write an equation to find the high and low temperatures.

• |t - 15| = -10

• |t - 15| = 10

• |t - 10| = 15

• |t + 10| = 15

A submarine can travel 175 feet below sea level, plus or minus 25 feet. Write an equation to represent this situation.

Hint: What kind of number represents below sea level?

• |x - 175| = 25

• |x + 175| = 25

• |x - 25| = 175

• |x + 25| = 175