Answer
$x=-9$
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 $15$ on both sides of the equation to obtain:
$15(\frac{3x}{5}) = 15(\frac{2x}{3}+1)
\\\frac{45x}{5} - \frac{30x}{3} +15
\\9x = 10x+15$
Subtract $9x$ and $15$ on both sides to obtain:
$-15=10x-9x
\\-15=x$
Check:
$\begin{array}{ccc}
&\frac{3(-15)}{5} &= &\frac{2(-15)}{3}+1
\\&\frac{-45}{5} &= &\frac{-30}{3}+1
\\&-9 &= &-10+1
\\&-9 &= &-9\end{array}$
