# Chapter 1 - Section 1.5 - Linear Inequalities in One Variable - 1.5 Exercises - Page 100: 47

$[-5,6]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-6 \le 2x+4 \le 16 ,$ 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} -6-4 \le 2x+4-4 \le 16-4 \\\\ -10 \le 2x \le 12 \\\\ -\dfrac{10}{2} \le \dfrac{2x}{2} \le \dfrac{12}{2} \\\\ -5 \le x \le 6 .\end{array} In interval notation, the solution set is $[-5,6] .$ The red graph is the graph of the solution set.

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