Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 27

$x=-22$

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{x-2}{4}=\dfrac{x+4}{3} ,$ is \begin{array}{l}\require{cancel} 3(x-2)=4(x+4) \\\\ 3x-6=4x+16 \\\\ 3x-4x=16+6 \\\\ -x=22 \\\\ x=-22 .\end{array}