# Chapter 9 - Inequalities and Problem Solving - 9.2 Intersections, Unions, and Compound Inequalities - 9.2 Exercise Set - Page 590: 52

$2\lt x \lt 8$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $-1\lt x-3 \lt 5 .$ Then graph. In the graph above, a hollowed dot is used for $\lt$ or $\gt$. A shaded dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} -1\lt x-3 \lt 5 \\\\ -1+3\lt x-3+3 \lt 5+3 \\\\ 2\lt x \lt 8 .\end{array} The graph includes the points from $2$ (exclusive) to $8$ (exclusive).

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