Multiply both sides by \(15\) (the LCM of \(3, 5\)).
\[5x-3(x-1)=9\]
Expand.
\[5x-3x+3=9\]
Simplify \(5x-3x+3\) to \(2x+3\).
\[2x+3=9\]
Subtract \(3\) from both sides.
\[2x=9-3\]
Simplify \(9-3\) to \(6\).
\[2x=6\]
Divide both sides by \(2\).
\[x=\frac{6}{2}\]
Simplify \(\frac{6}{2}\) to \(3\).
\[x=3\]
x=3
