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: 64

Answer

The solution set is $(-\infty, 5)$. 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 positive number is multiplied to each side of an inequality, the inequality's direction/sense does not change. 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 $a+c \ge b+c$ On the left side of the inequality, distribute $-3$ to each term of the binomial to obtain: $\begin{array}{ccc} &-3(1)-(-3(x) &\lt &12 \\&-3+3x &\lt &12 \end{array}$ Use the rule in (2) above by adding $3$ to both sides of the inequality to obtain: $\begin{array}{ccc} &-3+3x+3 &\lt &12+3 \\&3x &\lt &15 \end{array}$ Use the rule in (1) above by multiplying $\frac{1}{3}$ to both sides of the inequality to obtain: $\begin{array}{ccc} &\frac{1}{3}(3x) &\lt &\frac{1}{3}(15) \\&x &\lt &5 \end{array}$ Thus, the solution set is $(-\infty, 5)$.
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