Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 46

$x\lt-2$

Multiplying both sides by the $LCD= 56 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{x-6}{8}-\dfrac{x+2}{7}\gt-1 ,$ is \begin{array}{l}\require{cancel} 7(x-6)-8(x+2)\gt56(-1) \\\\ 7x-42-8x-16\gt-56 \\\\ 7x-8x\gt-56+42+16 \\\\ -x\gt2 \\\\ x\lt-2 .\end{array}