Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 21

$x\lt\dfrac{5}{2}$

Using the properties of inequalities, the solution to the given inequality, $ -2(x+6)\gt-17 ,$ is \begin{array}{l}\require{cancel} (x+6)\lt\dfrac{-17}{-2} \\\\ x+6\lt\dfrac{17}{2} \\\\ x\lt\dfrac{17}{2}-6 \\\\ x\lt\dfrac{17}{2}-\dfrac{12}{2} \\\\ x\lt\dfrac{5}{2} .\end{array}