Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Mixed Review Exercises: 10


$\left( -\infty,\dfrac{14}{17} \right)$

Work Step by Step

Using the properties of inequality, the given inequality, $ \dfrac{3}{4}(x-2)-\dfrac{1}{3}(5-2x)\lt-2 ,$ simplifies to \begin{array}{l}\require{cancel} 12\left[ \dfrac{3}{4}(x-2)-\dfrac{1}{3}(5-2x)\right]\lt(-2)12 \\\\ 9(x-2)-4(5-2x)\lt-24 \\\\ 9x-18-20+8x\lt-24 \\\\ 9x+8x\lt-24+18+20 \\\\ 17x\lt14 \\\\ x\lt\dfrac{14}{17} .\end{array} Hence, the solution is the interval $ \left( -\infty,\dfrac{14}{17} \right) .$
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