#### Answer

$\left[\dfrac{11}{12}, \dfrac{13}{6}\right]$
Refer to the image below for the graph.

#### Work Step by Step

Multiply the LCD of $20$ to each part of the inequality to eliminate the fractions:
$\begin{array}{ccccc}
&20\left(-\dfrac{1}{2}\right) &\le &20\left(\dfrac{4-3x}{5}\right) &\le &20\left(\dfrac{1}{4}\right)
\\&-10 &\le &4(4-3x) &\le &5
\\&-10 &\le &16-12x &\le &5
\end{array}$
Subtract $16$ to each part of the inequality to obtain:
$\begin{array}{ccccc}
&-10-16 &\le &16-12x-16 & \le &5-16
\\&-26 &\le &-12x &\le &-11
\end{array}$
Divide each part by $-12$
Note that this will affect the inequality symbols as they will flip to the opposite direction.
$\begin{array}{ccccc}
&\dfrac{-26}{-12} &\ge &\dfrac{-12x}{-12} &\ge &\dfrac{-11}{-12}
\\&\dfrac{13}{6} &\ge &x &\ge &\dfrac{11}{12}
\end{array}$
This inequality is equivalent to:
$\dfrac{11}{12}\le x \le \dfrac{13}{6}$
Thus, the solution set is $\bf\left[\dfrac{11}{12}, \dfrac{13}{6}\right]$.
To graph this solution set, plot solid dots at $\dfrac{11}{12}$ (or 0.9167) and $\dfrac{13}{6}$
(or 2.1667) then shade the region in between.
(refer to the attached image in the answer part above for the graph)