Answer
$ x=-\frac{4}{5}$.
Work Step by Step
The given expression is
$\Rightarrow \frac{2}{3}(x+5)=\frac{1}{4}x+3$
Multiply by the LCD $=12$.
$\Rightarrow 12\left [\frac{2}{3}\left (x+5\right ) \right]=12\left ( \frac{1}{4}x+3 \right )$
Use distributive property.
$\Rightarrow 12\left [\frac{2}{3}\left (x+5\right ) \right]=12\left ( \frac{1}{4}x\right )+12(3) $
Simplify.
$\Rightarrow 8\left (x+5\right )=3x+36 $
Use distributive property.
$\Rightarrow 8(x)+8(5)=3x+36 $
Simplify.
$\Rightarrow 8x+40=3x+36 $
Add $-3x-40$ to both sides.
$\Rightarrow 8x+40-3x-40=3x+36-3x-40$
Simplify.
$\Rightarrow 5x=-4$
Divide both sides by $5$.
$\Rightarrow \frac{5x}{5}=-\frac{4}{5} $
Simplify.
$\Rightarrow x=-\frac{4}{5}$.
