Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Test - Page 185: 5

$x=-77$

Multiplying both sides by the $LCD= 30 $ and then using the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{x-1}{6}-\dfrac{x+2}{5}=2 ,$ is \begin{array}{l}\require{cancel} 5(x-1)-6(x+2)=30(2) \\\\ 5x-5-6x-12=60 \\\\ 5x-6x=60+5+12 \\\\ -x=77 \\\\ x=-77 .\end{array}