Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.4 Linear Inequalities in One Variable - Exercise Set 6.4 - Page 384: 73


\[\left\{ x|x\le 14 \right\}\]

Work Step by Step

Let us suppose the number is\[x\]. Then, the algebraic form of the inequality is \[2\left( 4+x \right)\le 36\] Now, find out possible values of \[x\] satisfying the inequality and the inequality is solved as follows: \[\begin{align} & 2\left( 4+x \right)\le 36 \\ & 4+x\le 18 \\ & x\le 14 \\ \end{align}\] Hence, all the real numbers less than or equal to 14 will satisfy the condition. The set-builder form of the inequality is obtained as follows: \[\left\{ x|x\le 14 \right\}\]
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