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: 27

Answer

$(-\infty,\frac{3}{5}]$

Work Step by Step

$\frac{1}{4}(3x+2)-x\geq\frac{3}{8}(x-5)+2$ Mutiply both sides of the equation by 8, the least common multiple, to eliminate fractions. $8(\frac{1}{4}(3x+2))-8(x)\geq8(\frac{3}{8}(x-5))+8(2)$ Simplify. Apply the distributive property. Combine like terms. $2(3x+2)-8x\geq3(x-5)+16$ $6x+4-8x\geq3x-15+16$ $4-2x\geq3x+1$ Add 2x to each side of the equation. Subtract 1 from each side. $4-2x+2x\geq3x+1+2x$ $4\geq5x+1$ $4-1\geq5x+1-1$ $3\geq5x$ Divide both sides by 5. $3\div5\geq5x\div5$ $\frac{3}{5}\geq x$ $x\leq\frac{3}{5}$ This is written in interval notation as $(-\infty,\frac{3}{5}]$ where ] indicates that $\frac{3}{5}$ is included in the solution set for x.
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