Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 1 - Expressions, Equations, and Inequalities - 1-6 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 47: 79

Answer

sometimes

Work Step by Step

As long as $x + 2$ is positive or zero, the statement is true. For example: If $x = 3$, $|x + 2| = |3 + 2| = |5| = 5\\$ while $\\x + 2 = 3 + 2 = 5$ And so in this case, $|x + 2| = x + 2$ because $5$ is indeed equal to $5$. But, if $x + 2$ comes out negative, the statement is false. For example, let’s say $x = –3$, then: $|x + 2| = |–3 + 2| = |–1| = 1\\$ while $x + 2 = –3 + 2 = –1$ And $1\ne -1$ Therefore, the given statement is only sometimes true.
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