#### Answer

$\color{blue}{(-\frac{13}{4}, \frac{3}{4}]}$

#### Work Step by Step

Multiply $-2$ to each part.
Note that since a negative number is multiplied to the inequality, the inequality symbols will be reversed.
\begin{array}{ccccc}
&-2(1)&\ge &-2 \cdot \dfrac{4x-5}{-2} &\gt &-2(9)
\\&-2 &\ge &4x-5 &\gt &-18
\end{array}
Add $5$ to each part:
\begin{array}{ccccc}
\\&-2+5 &\ge &4x-5+5 &\gt &-18+5
\\&3 &\ge &4x &\ge &-13
\end{array}
Divide each part by $4$:
\begin{array}{ccccc}
\\&\frac{3}{4} &\ge &\frac{4x}{4} &\gt &\frac{-13}{4}
\\&\frac{3}{4} &\ge &x &\gt &\frac{-13}{4}
\end{array}
This inequality is equivalent to:
$-\frac{13}{4} \lt x \le \frac{3}{4}$
Thus, the solution to the given inequality is:
$\color{blue}{(-\frac{13}{4}, \frac{3}{4}]}$