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EXAMPLE 5 - PowerPoint PPT Presentation


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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. 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

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STEP2

Solve the inequality.

ANSWER

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

Add 5.125 to each expression.

slide3

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

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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

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STEP3

Write a verbal model. Then write an inequality.

ANSWER

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

EXAMPLE 6

Write a range as an absolute value inequality

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ANSWER

–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.

slide7

ANSWER

–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.

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ANSWER

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

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ANSWER

A mat is unacceptable if its thickness tsatisfies |t – 7.875| > 0.375.

for Examples 5 and 6

GUIDED PRACTICE

13.Gymnastics: For Example 6, write an absolute value inequality describing the unacceptable mat thicknesses.