#### Answer

$x=10$

#### Work Step by Step

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}