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: 63

Answer

The solution set is $(-7, +\infty)$. Refer to the image below for the graph.
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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's direction/sense change to its opposite. Thus, if $a \lt b$ and $c\lt 0$, then $ac \gt bc$. (2) The addition property of inequalities states that If $a \ge b$, then $a+c \ge b+c$ Use the rule in (1) above by multiplying $-\frac{1}{2}$to both sides of the inequality to obtain: $\begin{array}{ccc} &-\frac{1}{2}(-2(x+3)) &\gt &-\frac{1}{2}(8) \\&x+3 &\gt &-4 \end{array}$ Use the rule in (2) above by adding $-3$ to both sides of the inequality to obtain: $\begin{array}{ccc} &x+3 + (-3) &\gt &-4+(-3) \\&x &\gt &-7 \end{array}$ Thus, the solution set is $(-7, +\infty)$.
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