Explanation Given: The inequality is | x − 3 | = | x − 2 | + 1 . Calculation: The inequality is | x − 3 | = | x − 2 | + 1 . There are three cases. Case 1: If x ≥ 3 , both absolute values are positive. Then, x − 3 = x − 2 + 1 − 3 = − 1 Thus, there is no solution. Case 2: If 2 ≤ x < 3 , then x − 3 < 0 and x − 2 ≥ 0 . Now, the equation becomes. 3 − x = x − 2 + 1 − x − x = − 2 + 1 − 3 − 2 x = − 4 x = 2 Thus, the solution is 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.1, Problem 26E

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Solve the set of real numbers satisfying |x−3|=|x−2|+1 as a half-infinite interval.

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Chapter 1.1, Problem 25E

Chapter 1.1, Problem 27E

Chapter 1 Solutions

Calculus - Standalone book

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Solve the set of real numbers satisfying | x − 3 | = | x − 2 | + 1 as a half-infinite interval.

Solution Summary: The author explains that the inequality is x-3right|=left|x-2 right|+1.

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Solve the set of real numbers satisfying |x−3|=|x−2|+1 as a half-infinite interval.

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Chapter 1 Solutions