#### Answer

$x=-7$

#### Work Step by Step

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}