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: 75


\[\left\{ x\le 50 \right\}\].

Work Step by Step

Let us suppose the number is \[x\]. Then, the algebraic form of the inequality is: \[\frac{3x}{5}\,+4\,\le 34\] And now to find out possible values of \[x\] satisfying the inequality the inequality is solved as follows: \[\begin{align} & \frac{3x}{5}\,+4\,\le 34 \\ & \frac{3x\times 5}{5}\,+4\times 5\,\le 34\times 5 \\ & 3x\,+20\le 170 \end{align}\] This can be further simplified as: \[\begin{align} & 3x\le 150 \\ & \frac{3x}{3}\le \frac{150}{3} \\ & x\le \text{ }50 \end{align}\] Hence all the real numbers less than or equal to 50 will satisfy the condition. The set-builder form of the inequality obtained is: \[\left\{ x\,x\le \,50 \right\}\] Therefore, the number can be represented in set builder form as \[\left\{ x\le 50 \right\}\].
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