# Chapter 1 - Section 1.5 - Linear Inequalities in One Variable - 1.5 Exercises: 48

$(-7,-6)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-15 \lt 3x+6 \lt -12 ,$ use the properties of inequality. For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$ For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -15-6 \lt 3x+6-6 \lt -12-6 \\\\ -21 \lt 3x \lt -18 \\\\ -\dfrac{21}{3} \lt \dfrac{3x}{3} \lt -\dfrac{18}{3} \\\\ -7 \lt x \lt -6 .\end{array} In interval notation, the solution set is $(-7,-6) .$ The red graph is the graph of the solution set.

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