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: 15

Answer

$3\frac{3}{4}\lt x\lt8\frac{1}{2}$
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Work Step by Step

$\frac{1}{4}\lt\frac{2x-7}{2}\lt5\longrightarrow$ multiply all 3 parts by 2 $\frac{1}{4}\times2\lt\frac{2x-7}{2}\times2\lt5\times2\longrightarrow$ multiply $\frac{1}{2}\lt2x-7\lt10\longrightarrow$ add 7 to all 3 parts $\frac{1}{2}+7\lt2x-7+7\lt10+7\longrightarrow$ add $7\frac{1}{2}\lt 2x\lt17\longrightarrow$ divide all 3 parts by 2 $7\frac{1}{2}\div2\lt2x\div 2\lt17\div 2\longrightarrow$ divide $3\frac{3}{4}\lt x\lt8\frac{1}{2}$
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