# Chapter 1, Equations and Graphs - Section 1.7 - Solving Inequalities - 1.7 Exercises: 29

$[4.5, 5)$ Refer to the image below for the graph.

#### Work Step by Step

Subtract $8$ to each part of the inequality to obtain: $\begin{array}{ccccc} &-2-8 &\lt &8-2x-8 &\le &-1-8 \\&-10 &\lt &-2x &\le &-9 \end{array}$ Divide $-2$ to each part of the inequality. Note that doing this will affect the inequality symbols as they will flip to the opposite direction: $\begin{array}{ccccc} &\dfrac{-10}{-2} &\gt &\dfrac{-2x}{-2} &\ge &\dfrac{-9}{-2} \\&5 &\gt &x &\ge &4.5 \end{array}$ This inequality is equivalent to: $4.5 \le x \lt 5$ Thus, the solution set is $\bf[4.5, 5)$. To graph this solution set, plot a solid dot at $4.5$ and a hole (or hollow dot) at $5$ then shade the region in between. (refer to the attached image in the answer part above for the graph)

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