2x + (x-1)/2 = (5x-3)/3

This can be written as

$$2x+\frac{x-1}{2}=\frac{5x-3}{3}\\\\
2x+\frac{x}{2}-\frac{1}{2}= \frac{5x}{3}-1\\\\$$

Add 1/2 to both sides and subtract 5x/3 from both sides

$$2x+\frac{x}{2}-\frac{5x}{3}=-\frac{1}{2}$$

Collect the x terms over a common denominator

$$\frac{12x+3x-10x}{6}=-\frac{1}{2}\\\\
\frac{5x}{6}=-\frac{1}{2}$$

Multiply both sides by 6/5

$$x=-\frac{3}{5}$$