Intermediate Algebra (6th Edition)

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

Chapter 2 - Sections 2.1-2.4 - Integrated Review - Linear Equations and Inequalities - Page 88: 28

Answer

$(-\infty,-\frac{19}{32})$

Work Step by Step

$\frac{1}{3}(x-10)-4x\gt\frac{5}{6}(2x+1)-1$ Multiply both sides of the equation by 6, the least common multiple, to eliminate fractions. $6(\frac{1}{3}(x-10))-6(4x)\gt6(\frac{5}{6}(2x+1))-6(1)$ Simplify. Apply the distributive property. Combine like terms. $2(x-10)-24x\gt5(2x+1)-6$ $2x-20-24x\gt10x+5-6$ $-22x-20\gt10x-1$ Subtract 10x from each side. Add 20 to each side. $-22x-20-10x\gt10x-1-10x$ $-32x-20\gt-1$ $-32x-20+20\gt-1+20$ $-32x\gt19$ Divide both sides by -32. The inequality sign must be reversed when multiplying by a negative. $-32x\div-32\lt19\div-32$ $x\lt-\frac{19}{32}$ This is written in interval notation as $(-\infty,-\frac{19}{32})$ Where ) indicates that the solution set for x approaches, but does not include, $-\frac{19}{32})$.
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