#### Answer

$x=-12$

#### Work Step by Step

For easier work, it is better to get rid of the fractions.
This can be achieved by multiplying the LCD of $12$ on both sides of the equation to obtain:
$12(\frac{x}{4}) = 12(2+\frac{x-3}{3})
\\\frac{12(x)}{4} = 12(2) +\frac{12(x-3)}{3}
\\3x = 24 + 4(x-3)
\\3x = 24+4x-12
\\3x=4x+12$
Subtract $3x$ and $12$ on both sides to obtain:
$-12=4x-3x
\\-12=x$
Check:
$\begin{array}{ccc}
&\frac{-12}{4} &= &2+\frac{-12-3}{3}
\\&-3 &= &2+\frac{-15}{3}
\\&-3 &= &2 + (-5)
\\&-3 &= &-3\end{array}$