Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - 3-6 Compound Inequalities - Practice and Problem-Solving Exercises - Page 205: 41


$-4\frac{1}{12}\leq w\lt12\frac{1}{4}$

Work Step by Step

$-\frac{4}{3}\leq\frac{1}{7}w-\frac{3}{4}\lt1\longrightarrow$ using the addition property of inequality, add $\frac{3}{4}$ to each part $-\frac{4}{3}+\frac{3}{4}\leq\frac{1}{7}w-\frac{3}{4}+\frac{3}{4}\lt1+\frac{3}{4}\longrightarrow$ add $-\frac{7}{12}\leq\frac{1}{7}w\lt1\frac{3}{4}\longrightarrow$ using the multiplication property of inequality, multiply each part by 7 $-\frac{7}{12}\times7\leq\frac{1}{7}w\times7\lt1\frac{3}{4}\times7\longrightarrow$ simplify $-4\frac{1}{12}\leq w\lt12\frac{1}{4}$
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