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: 38

Answer

The solution is $\Big[1,\dfrac{11}{3}\Big]$

Work Step by Step

$|7-3x|\le4$ Solving this absolute value inequality is equivalent to solving the following inequality: $-4\le7-3x\le4$ $\textbf{Solve the inequality shown above:}$ $-4\le7-3x\le4$ Subtract $7$ from all three parts of the inequality: $-4-7\le7-7-3x\le4-7$ $-11\le-3x\le-3$ Divide all three parts of the inequality by $-3$ and reverse the inequality signs: $\dfrac{-11}{-3}\ge\dfrac{-3x}{-3}\ge\dfrac{-3}{-3}$ $\dfrac{11}{3}\ge x\ge1$ Expressing the solution in interval notation: $\Big[1,\dfrac{11}{3}\Big]$
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