Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 183: 14

$x=10$

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{4x+5}{5}=\dfrac{3(x-4)}{2} ,$ is \begin{array}{l}\require{cancel} 2(4x+5)=5(3)(x-4) \\\\ 8x+10=15x-60 \\\\ 8x-15x=-60-10 \\\\ -7x=-70 \\\\ x=\dfrac{-70}{-7} \\\\ x=10 .\end{array}