Answer
$x= -\frac{37}{2}$.
Work Step by Step
The given expression is
$\Rightarrow \frac{7}{10}x-\frac{4}{5}=\frac{5}{6}(x+2)$
Multiply by the LCD $=30$.
$\Rightarrow 30\left ( \frac{7}{10}x-\frac{4}{5} \right )=30\left [\frac{5}{6}\left (x+2\right ) \right]$
Use distributive property.
$\Rightarrow 30\left ( \frac{7}{10}x\right )-30\left (\frac{4}{5} \right )=30\left [\frac{5}{6}\left (x+2\right ) \right]$
Simplify.
$\Rightarrow 21x-24=25\left (x+2\right ) $
Use distributive property.
$\Rightarrow 21x-24=25(x)+25(2) $
Simplify.
$\Rightarrow 21x-24=25x+50 $
Add $-50-21x$ to both sides.
$\Rightarrow 21x-24-50-21x=25x+50-50-21x $
Simplify.
$\Rightarrow -74=4x $
Divide both sides by $4$.
$\Rightarrow -\frac{74}{4}=\frac{4x}{4} $
Simplify.
$\Rightarrow -\frac{37}{2}=x$.
