Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises: 34

Answer

The solution is $(-\infty,-3)\cup(1,\infty)$

Work Step by Step

$5|x+1|\gt10$ Take $5$ to divide the right side: $|x+1|\gt\dfrac{10}{5}$ $|x+1|\gt2$ Solving this absolute value inequality is equivalent to solving two separate inequalities, which are: $x+1\gt2$ and $x+1\lt-2$ $\textbf{Solve the first inequality:}$ $x+1\gt2$ Take $1$ to the right side: $x\gt2-1$ $x\gt1$ $\textbf{Solve the second inequality:}$ $x+1\lt-2$ Take $1$ to the right side: $x\lt-2-1$ $x\lt-3$ Expressing the solution in interval notation: $(-\infty,-3)\cup(1,\infty)$
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