EXAMPLE 5

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# EXAMPLE 5 - PowerPoint PPT Presentation

Baseball. A professional baseball should weigh 5.125 ounces, with a tolerance of 0.125 ounce. Write and solve an absolute value inequality that describes the acceptable weights for a baseball. STEP 1. Write a verbal model. Then write an inequality. EXAMPLE 5.

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Baseball

A professional baseball should weigh 5.125 ounces, with a tolerance of 0.125 ounce. Write and solve an absolute value inequality that describes the acceptable weights for a baseball.

STEP1

Write a verbal model. Then write an inequality.

EXAMPLE 5

Solve an inequality of the form |ax + b| ≤ c

SOLUTION

STEP2

Solve the inequality.

So, a baseball should weigh between 5 ounces and 5.25 ounces, inclusive. The graph is shown below.

EXAMPLE 5

Solve an inequality of the form |ax + b| ≤ c

|w – 5.125| ≤ 0.125

Write inequality.

Write equivalent compound inequality.

– 0.125 ≤ w – 5.125 ≤ 0.125

5 ≤ w ≤ 5.25

Gymnastics

The thickness of the mats used in the rings, parallel bars, and vault events must be between 7.5 inches and 8.25 inches, inclusive. Write an absolute value inequality describing the acceptable mat thicknesses.

Calculate the mean of the extreme mat thicknesses.

STEP1

EXAMPLE 6

Write a range as an absolute value inequality

SOLUTION

Mean of extremes ==7.875

STEP2

Find the tolerance by subtracting the mean from the upper extreme.

7.5 + 8.25

2

EXAMPLE 6

Write a range as an absolute value inequality

Tolerance = 8.25 –7.875

=0.375

STEP3

Write a verbal model. Then write an inequality.

A mat is acceptable if its thickness tsatisfies |t – 7.875| ≤ 0.375.

EXAMPLE 6

Write a range as an absolute value inequality

–8 <x <4

for Examples 5 and 6

GUIDED PRACTICE

Solve the inequality. Then graph the solution.

10. |x + 2| < 6

The solutions are all real numbers less than – 8 or greater than 4. The graph is shown below.

–5 ≤x ≤4

for Examples 5 and 6

GUIDED PRACTICE

Solve the inequality. Then graph the solution.

11. |2x + 1| ≤ 9

The solutions are all real numbers less than –5 or greater than 4. The graph is shown below.

3 ≤x ≤11

The solutions are all real numbers less than 3 or greater than 11. The graph is shown below.

for Examples 5 and 6

GUIDED PRACTICE

Solve the inequality. Then graph the solution.

12. |7 – x| ≤ 4