Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 183: 13

$x=-7$

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{4(x+1)}{3}=\dfrac{3x+5}{2} ,$ is \begin{array}{l}\require{cancel} 2(4)(x+1)=3(3x+5) \\\\ 8x+8=9x+15 \\\\ 8x-9x=15-8 \\\\ -x=7 \\\\ x=-7 .\end{array}