Explanation Given Information: The provided inequality is | 0.5 x − 3.5 | + 0.2 ≥ 0.6 . Formula used: Let k be a positive real number. Then, to solve the inequality | a x + b | ≥ k is same as solving two compound inequality; a x + b ≥ k or a x + b ≤ − k Calculation: Consider the inequality | 0.5 x − 3.5 | + 0.2 ≥ 0.6 . Add − 0.2 on both sides of the inequality. | 0.5 x − 3.5 | + 0.2 − 0.2 ≥ 0.6 − 0.2 | 0.5 x − 3.5 | + 0.2 − 0.2 ≥ 0.4 | 0.5 x − 3.5 | ≥ 0.4 By using the formula the inequality is written as follows, 0.5 x − 3.5 ≥ 0.4 or 0.5 x − 3.5 ≤ − 0.4 Take the inequality 0.5 x − 3.5 ≥ 0.4 , Add 3.5 on both sides of the inequality. 0.5 x − 3.5 + 3.5 ≥ 0.4 + 3.5 0.5 x − 3.5 + 3.5 ≥ 3.9 0.5 x ≥ 3.9 Divide by 0.5 on both sides of the inequality. 0.5 x 0.5 ≥ 3.9 0.5 x ≥ 7.8 Now take the inequality 0.5 x − 3.5 ≤ − 0.4 . Add 3.5 on both sides of the inequality. 0.5 x − 3.5 + 3.5 ≤ − 0.4 + 3.5 0.5 x − 3.5 + 3.5 ≤ 3.1 0.5 x ≤ 3.1 Divide by 0.5 on both sides of the inequality. 0.5 x 0.5 ≤ 3.1 0.5 x ≤ 6.2 The inequalities are x ≥ 7.8 or x ≤ 6.2 . Since the inequality contains less than symbol so the points are not included in the solution set. The solution set of the inequalityis ( − ∞ , 6.2 ] ∪ [ 7.8 , ∞ ) . Check: Put the value of x = 6.2 in the inequality | 0.5 x − 3.5 | + 0.2 ≥ 0.6 ; | 0.5 ( 6.2 ) − 3.5 | + 0.2 ≥ ? 0.6 | − 0

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 8.3, Problem 88E

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To calculate: Thesolution set of the inequality | 0.5x−3.5 |+0.2≥0.6.

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Chapter 8.3, Problem 87E

Chapter 8.3, Problem 89E

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Chapter 8 Solutions

Beginning and Intermediate Algebra (6th Edition)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Solve each inequality. Give the solution set in...Ch. 8.1 - Prob. 10E

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Thesolution set of the inequality | 0.5 x − 3.5 | + 0.2 ≥ 0.6 .

Solution Summary: The author calculates the solution set of the inequality left|0.5x-3.5right|+0.2ge 0.6.

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To calculate: Thesolution set of the inequality | 0.5x−3.5 |+0.2≥0.6.

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Chapter 8 Solutions