Answer
$$\frac{1}{4}x -\frac{5}{3}. $$
Work Step by Step
We simplify by removing the parentheses and then combining the like terms as follows: $$ \left(\frac{3}{4}x -1\right)+\left( -\frac{1}{2}x-\frac{2}{3} \right)= \frac{3}{4}x -1-\frac{1}{2}x-\frac{2}{3} \\ = \frac{1}{4}x -\frac{5}{3}. $$
