Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 183: 9

$x=10$

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{x-1}{-3}=\dfrac{x+2}{-4} ,$ is \begin{array}{l}\require{cancel} -4(x-1)=-3(x+2) \\\\ -4x+4=-3x-6 \\\\ -4x+3x=-6-4 \\\\ -x=-10 \\\\ x=10 .\end{array}