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: 74


\[\left\{ x\le 11 \right\}\].

Work Step by Step

Let us suppose the number is \[x\]. Then, the algebraic form of the inequality is: \[3\left( 5+x \right)\le 48\] And now to find out possible values of \[x\] satisfying the inequality the inequality is solved as follows: \[\begin{align} & 3\left( 5+x \right)\le 48 \\ & 5+x\le 16 \\ & x\le 11 \end{align}\] Hence all the real numbers less than or equal to 11 will satisfy the condition. The set-builder form of the inequality obtained is: \[\left\{ x|x\le 11 \right\}\] The set-builder notation for all real numbers that satisfy the given condition is\[\left\{ x\le 11 \right\}\].
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