Answered: Prove that –(|a| + |b|) ≤ a + b ≤ |a|+…

Prove that –(|a| + |b|) ≤ a + b ≤ |a|+ |b| for any real numbers a and b. (Hint: Use cases when a,b,≥ 0;a,b < 0; and a & b have different signs.)

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter10: Inequalities

Section10.2: Solving Inequalities

Problem 51WE

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Question

Prove that –(|a| + |b|) ≤ a + b ≤ |a|+ |b| for any real numbers a and b.

(Hint: Use cases when a,b,≥ 0;a,b < 0; and a & b have different signs.)

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