## College Algebra (11th Edition)

Published by Pearson

# Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises - Page 154: 42

#### Answer

The equation is an identity, true for all real values of $x$.

#### Work Step by Step

The equation $|x|=\sqrt{x^{2}}$ has infinitely many solutions because if we solve it, we get an identity: $|x|$ implies: $|x|=x$ (if x is positive) or $|x|=-x$ (if x is negative) Similarly: $\sqrt{x^{2}}$ implies: $\sqrt{x^{2}}=x$ (if x is positive) or $\sqrt{x^{2}}=-x$ (if x is negative) Hence the two sides equal each other (identity). In other words, the equation is true for all real values of $x$ (infinite solutions).

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.