The given expression is
[tex]\frac{1}{2}x-3=2-\frac{3}{4}x[/tex]First, we add 3/4x to each side
[tex]\begin{gathered} \frac{3}{4}x+\frac{1}{2}x-3=2-\frac{3}{4}x+\frac{3}{4}x \\ \frac{6x+4x}{8}-3=2 \\ \frac{10x}{8}=3+2 \\ \frac{5x}{4}=5 \\ 5x=5\cdot4 \\ x=4 \end{gathered}[/tex]