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: 62

Answer

The solution set is $[5, +\infty)$. 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 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) The addition property of inequalities states that If $a \ge b$, then $a+c \ge b+c$ Use the rule in (2) above by adding $2$ and $-x$ on each side to obtain: $\begin{array}{ccc} &2x-2+2-x &\ge &3+x+2+(-x) \\&(2x-x)+(-2+2) &\ge &(x-x)+(3+2) \\&x &\ge &5 \end{array}$ Thus, the solution set is $[5, +\infty)$.
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