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 - Page 167: 41


The solution is $(-101,-99)$

Work Step by Step

$|0.01x+1|\lt0.01$ Solving this absolute value inequality is equivalent to solving the following inequality: $-0.01\lt0.01x+1\lt0.01$ $\textbf{Solve the inequality shown above:}$ $-0.01\lt0.01x+1\lt0.01$ Subtract $1$ from all three parts of the inequality: $-0.01-1\lt0.01x+1-1\lt0.01-1$ $-1.01\lt0.01x\lt-0.99$ Divide all three parts of the inequality by $0.01$: $-\dfrac{1.01}{0.01}\lt\dfrac{0.01x}{0.01}\lt-\dfrac{0.99}{0.01}$ $-101\lt x\lt-99$ Expressing the solution in interval notation: $(-101,-99)$
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