College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.7 - Solving Inequalities - 1.7 Exercises - Page 148: 24


$(-\infty, 11]$ Refer to the image below for the graph.

Work Step by Step

Distribute $2$ on the left side of the inequality to obtain: $14x-6 \le 12x+16$ Subtract $12x$ and add $6$to both sides of the inequality to obtain: $\begin{array}{ccc} &14x-6-12x+6 &\le &12x+16-12x+6 \\&2x &\le &22 \end{array}$ Divide $2$ to both sides of the inequality to obtain: $\begin{array}{ccc} \\&\dfrac{2x}{2} &\le & \dfrac{22}{2} \\&x &\le &11 \end{array}$ Thus, the solution set is $(-\infty, 11]$. To graph this solution set, plot a solid dot at $11$ then shade the region to its left. (refer to the attached image in the answer part above for the graph)
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