College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Review Exercises: 119

Answer

$\left( -\infty,-\dfrac{1}{7} \right)\cup\left( 1,\infty \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |7x-3|\gt4 ,$ use the definition of absolute value inequalities. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the inequality above is equivalent to \begin{array}{l}\require{cancel} 7x-3\gt4 \\\\\text{OR}\\\\ 7x-3\lt-4 .\end{array} Solving each inequality results to \begin{array}{l}\require{cancel} 7x-3\gt4 \\\\ 7x\gt4+3 \\\\ 7x\gt7 \\\\ x\gt\dfrac{7}{7} \\\\ x\gt1 \\\\\text{OR}\\\\ 7x-3\lt-4 \\\\ 7x\lt-4+3 \\\\ 7x\lt-1 \\\\ x\lt-\dfrac{1}{7} .\end{array} Hence, the solution set is the interval $ \left( -\infty,-\dfrac{1}{7} \right)\cup\left( 1,\infty \right) .$
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