Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 54

$x=-24$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{4(x+3)}{7}=\dfrac{2(x-6)}{5} ,$ is \begin{array}{l}\require{cancel} 4(5)(x+3)=2(7)(x-6) \\\\ 20x+60=14x-84 \\\\ 20x-14x=-84-60 \\\\ 6x=-144 \\\\ x=-\dfrac{144}{6} \\\\ x=-24 .\end{array}