Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Test - Page 146: 44

Answer

The solution set consist of all real numbers less than or equal to $12$.

Work Step by Step

Considered the inequality, $3\left( x+4 \right)\ge 5x-12$ , Apply Distributive law: $a\left( b+c \right)=ab+ac$ $\begin{align} & 3\left( x+4 \right)\ge 5x-12 \\ & 3x+3\times 4\ge 5x-12 \\ & 3x+12\ge 5x-12 \end{align}$ Subtract $12$ and $5x$ from both sides, $\begin{align} & 3x+12-12-5x\ge 5x-12-12-5x \\ & -2x\ge -24 \end{align}$ Multiply both sides by $-1$ (reverse the inequality right) $\left( -2x \right)\left( -1 \right)\le \left( -24 \right)\left( -1 \right)$ Divide both sides by $2$ $\begin{align} & \frac{2x}{2}\le \frac{24}{2} \\ & x\le 12 \end{align}$ The solution set consist of all real numbers less than or equal to $12$. The graph on the number line is shown below.
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