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EXAMPLE 5

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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EXAMPLE 5

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  1. 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

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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.

  7. 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.

  8. 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

  9. 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.

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