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: 36

Answer

The solution is $\Big(-\infty,1\Big)\cup\Big(\dfrac{11}{3},\infty\Big)$

Work Step by Step

$|7-3x|\gt4$ Solving this absolute value inequality is equivalent to solving two separate inequalities, which are: $7-3x\gt4$ and $7-3x\lt-4$ $\textbf{Solve the first inequality:}$ $7-3x\gt4$ Take $7$ to the right side: $-3x\gt4-7$ $-3x\gt-3$ Take $3$ to divide the right side and reverse the inequality sign: $x\lt\dfrac{-3}{-3}$ $x\lt1$ $\textbf{Solve the second inequality:}$ $7-3x\lt-4$ Take $7$ to the right side: $-3x\lt-4-7$ $-3x\lt-11$ Take $3$ to divide the right side and reverse the inequality sign: $x\gt\dfrac{-11}{-3}$ $x\gt\dfrac{11}{3}$ Expressing the solution in interval notation: $\Big(-\infty,1\Big)\cup\Big(\dfrac{11}{3},\infty\Big)$
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