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 204: 16

Answer

$33\geq q\geq-21$
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Work Step by Step

$-3\leq\frac{6-q}{9}\leq3\longrightarrow$ multiply all 3 parts by 9 $-3\times9\leq\frac{6-q}{9}\times9\leq3\times9\longrightarrow$ multiply $-27\leq6-q\leq27\longrightarrow$ subtract 6 from all 3 parts $-27-6\leq6-q-6\leq27-6\longrightarrow$ subtract $-33\leq -q\leq21\longrightarrow$ multiply all 3 parts by -1; reverse the inequality signs $-33\times-1\geq -q\times-1\geq 21\times-1\longrightarrow$ multiply $33\geq q\geq-21$ The graph has solid circles at the endpoints since 33 and -21 are included in the solution set.
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