EXAMPLE 5 Solve an inequality of the form

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EXAMPLE 5 Solve an inequality of the form |ax + b| ≤ c Baseball

EXAMPLE 5 Solve an inequality of the form |ax + b| ≤ c 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. SOLUTION STEP 1 Write a verbal model. Then write an inequality.

EXAMPLE 5 STEP 2 Solve an inequality of the form |ax + b| ≤

EXAMPLE 5 STEP 2 Solve an inequality of the form |ax + b| ≤ c Solve the inequality. |w – 5. 125| ≤ 0. 125 – 0. 125 ≤ w – 5. 125 ≤ 0. 125 5 ≤ w ≤ 5. 25 Write inequality. Write equivalent compound inequality. Add 5. 125 to each expression. ANSWER So, a baseball should weigh between 5 ounces and 5. 25 ounces, inclusive. The graph is shown below.

EXAMPLE 6 Write a range as an absolute value inequality Gymnastics The thickness of

EXAMPLE 6 Write a range as an absolute value inequality 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. SOLUTION STEP 1 Calculate the mean of the extreme mat thicknesses.

EXAMPLE 6 Write a range as an absolute value inequality 7. 5 + 8.

EXAMPLE 6 Write a range as an absolute value inequality 7. 5 + 8. 25 Mean of extremes = = 7. 875 2 STEP 2 Find the tolerance by subtracting the mean from the upper extreme. Tolerance = 8. 25 – 7. 875 = 0. 375

EXAMPLE 6 STEP 3 Write a range as an absolute value inequality Write a

EXAMPLE 6 STEP 3 Write a range as an absolute value inequality Write a verbal model. Then write an inequality. ANSWER A mat is acceptable if its thickness t satisfies |t – 7. 875| ≤ 0. 375.

GUIDED PRACTICE for Examples 5 and 6 Solve the inequality. Then graph the solution.

GUIDED PRACTICE for Examples 5 and 6 Solve the inequality. Then graph the solution. 10. |x + 2| < 6 ANSWER – 8 < x < 4 The solutions are all real numbers less than – 8 or greater than 4. The graph is shown below.

GUIDED PRACTICE for Examples 5 and 6 Solve the inequality. Then graph the solution.

GUIDED PRACTICE for Examples 5 and 6 Solve the inequality. Then graph the solution. 11. |2 x + 1| ≤ 9 ANSWER – 5 ≤ x ≤ 4 The solutions are all real numbers less than – 5 or greater than 4. The graph is shown below.

GUIDED PRACTICE for Examples 5 and 6 Solve the inequality. Then graph the solution.

GUIDED PRACTICE for Examples 5 and 6 Solve the inequality. Then graph the solution. 12. |7 – x| ≤ 4 ANSWER 3 ≤ x ≤ 11 The solutions are all real numbers less than 3 or greater than 11. The graph is shown below.

GUIDED PRACTICE 13. for Examples 5 and 6 Gymnastics: For Example 6, write an

GUIDED PRACTICE 13. for Examples 5 and 6 Gymnastics: For Example 6, write an absolute value inequality describing the unacceptable mat thicknesses. ANSWER A mat is unacceptable if its thickness t satisfies |t – 7. 875| > 0. 375.