Explanation Given: The equation is | 2 x − 1 | − | x + 5 | = 3 . Definition used: An absolute function is defined as, | x | = { x if x ≥ 0 − x if x < 0 . From the definition, the given equation is expressed as follows: | 2 x − 1 | = { 2 x − 1 if 2 x − 1 ≥ 0 − ( 2 x − 1 ) if 2 x − 1 < 0 and | x + 5 | = { x + 5 if x + 5 ≥ 0 − ( x + 5 ) if x + 5 < 0 . Simplify further as, | 2 x − 1 | = { 2 x − 1 if x ≥ 1 2 − 2 x + 1 if x < 1 2 and | x + 5 | = { x + 5 if x ≥ − 5 − x − 5 if x < − 5 . Therefore, there exist three cases such as, x < − 5 , − 5 ≤ x < 1 2 and x ≥ 1 2 . Case 1: If x < − 5 , solve the given equation for x as follows

Single Variable Calculus: Early Transcendentals

8th Edition

ISBN: 9781305270336

Author: James Stewart

Publisher: Cengage Learning

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Chapter 1, Problem 3P

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To solve: The equation |2x−1|−|x+5|=3.

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Chapter 1 Solutions

Single Variable Calculus: Early Transcendentals

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The equation | 2 x − 1 | − | x + 5 | = 3 .

Solution Summary: The author explains that the given equation is expressed as follows: x=-73and9.

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To solve: The equation |2x−1|−|x+5|=3.

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Chapter 1 Solutions