## Elementary Algebra

$x\lt-2$
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}