#### Answer

$x\le7$

#### Work Step by Step

Using the Distributive Property and the properties of inequality, the solution to the given inequality, $
\dfrac{4}{5}(3x+4)\le20
,$ is
\begin{array}{l}\require{cancel}
5\cdot\dfrac{4}{5}(3x+4)\le20\cdot5
\\\\
4(3x+4)\le100
\\\\
4(3x)+4(4)\le100
\\\\
12x+16\le100
\\\\
12x\le100-16
\\\\
12x\le84
\\\\
x\le\dfrac{84}{12}
\\\\
x\le7
.\end{array}