Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.1 - Equations and Inequalities Involving Absolute Value - Concept Quiz 11.1: 4

Answer

False

Work Step by Step

RECALL: $|a| = k \longrightarrow a = k \text{ or } a = -k$ Use the rule above to obtain: $|x-1| = 4 \longrightarrow x-1 = 4 \text{ or } x - 1 = -4$ Solve each equation to obtain: $x-1 = 4 \text{ or } x - 1 = -4 \\x = 4+1 \text{ or } x = -4+1 \\x = 5 \text{ or } x = -3$ Thus, the solution set of the given equation is $\left\{-3, 5\right\}$. Therefore, the given statement is false.
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