Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 12

$x\lt\dfrac{5}{4}$

Using the properties of inequalities, the solution to the given inequality, $ -x-2\gt3x-7 ,$ is \begin{array}{l}\require{cancel} -x-3x\gt-7+2 \\\\ -4x\gt-5 \\\\ x\lt\dfrac{-5}{-4} \\\\ x\lt\dfrac{5}{4} .\end{array}