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: 60

Answer

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 $a \gt b$ and $c\gt 0$, then $ac \gt bc$. (2) If $a \lt b$, then $a+c \lt b+c$ Use the rule in (2) above by adding $-5$ on each side to obtain: $\begin{array}{ccc} &2x+5+(-5) &\gt &1+(-5) \\&2x &\gt &-4 \end{array}$ Use rule the rule in (1) above by multiplying $\frac{1}{2}$ on both sides of the inequality to obtain $\begin{array}{ccc} &\frac{1}{2}(2x) &\gt &\frac{1}{2}(-4) \\&x &\gt &-2 \end{array}$ Thus, the solution set is $(-2, +\infty)$. To graph this on a number line, plot a hollow dot (or a hole) at $-2$, and then shade the region to its right.
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