#### Answer

$\color{blue}{[-\frac{16}{3}, \frac{19}{3}]}$

#### Work Step by Step

Multiply $-5$ to each part.
Note that since a negative number is multiplied to the inequality, the inequality symbols will be reversed.
\begin{array}{ccccc}
&-5(-3)&\ge &-5 \cdot \dfrac{3x-4}{-5} &\ge &-5(4)
\\&15 &\ge &3x-4 &\ge &-20
\end{array}
Add $4$ to each part:
\begin{array}{ccccc}
\\&15+4 &\ge &3x-4+4 &\ge &-20+4
\\&19 &\ge &3x &\ge &-16
\end{array}
Divide each part by $3$:
\begin{array}{ccccc}
\\&\frac{19}{3} &\ge &\frac{3x}{3} &\ge &\frac{-16}{3}
\\&\frac{19}{3} &\ge &x &\ge &\frac{-16}{3}
\end{array}
This inequality is equivalent to:
$-\frac{16}{3} \le x \le \frac{19}{3}$
Thus, the solution to the given inequality is:
$\color{blue}{[-\frac{16}{3}, \frac{19}{3}]}$