College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.5 - Solving Inequalities - 1.5 Assess Your Understanding - Page 128: 58


Refer to the image below for the graph.

Work Step by Step

RECALL: (1) The Multiplication Property of Inequality states that if a negative number is multiplied to each side of an inequality, the inequality changes direction/sense. Thus, if $a \le b$ and $c\lt 0$, then $ac \ge bc$. (2) If $a \lt b$, then $a-c \lt b-c$ Subtract $2$ to both sides of the inequality to obtain: $\begin{array}{ccc} &2-3x-2 &\le &5-2 \\&-3x &\le &3 \end{array}$ Multiply $-\frac{1}{3}$ on both sides of the inequality. Note that the inequality will change direction to its opposite. $\begin{array}{ccc} &-\frac{1}{3}(-3x) &\ge &-\frac{1}{3}(3) \\&x &\ge &-1 \end{array}$ Thus, the solution set is $[-1, +\infty)$. To graph this on a number line, plot a solid dot at $-1$ and then shade the region to its right.
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