Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set - Page 95: 88

Answer

$x=4$

Work Step by Step

The given inequality, $ 7x-1\le7+5x\le3(1+2x) ,$ is equivalent to \begin{array}{l}\require{cancel} 7x-1\le7+5x \text{ and } 7+5x\le3(1+2x) .\end{array} Solving the inequalities separately results to \begin{array}{l}\require{cancel} 7x-1\le7+5x \\ 7x-5x\le7+1 \\ 2x\le8 \\ x\le\dfrac{8}{2} \\ x\le4 \\\\\text{ and } \\\\ 7+5x\le3(1+2x) \\ 7+5x\le3+6x \\ 5x-6x\le3-7 \\ -x\le-4 \\ x\ge\dfrac{-4}{-1} \\ x\ge4 .\end{array} Since "and" is used, then the solution set is the intersection of the two inequalities. Hence, the solution set is $ x=4 .$
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