Simplify this expression: $$\left(2x+\frac{3}{2} (4x-6)\right)-4\left( -(2-x)+\frac{x}{2}\right)$$
To simplify this expression, I need to apply the distributive property and combine like terms. First, I'll distribute the $\frac{3}{2}$ to the parentheses on the left: $$2x+\frac{3}{2}(4x-6)-4\left( -(2-x)+\frac{x}{2}\right) = 2x+6x-9-4\left( -(2-x)+\frac{x}{2}\right)$$ Next, I'll distribute the $-4$ to the parentheses on the right: $$2x+6x-9-4\left( -(2-x)+\frac{x}{2}\right) = 2x+6x-9+8-4x-2x$$ Now I have all the terms in one line, so I can combine the ones that have the same variable or are constant: $$2x+6x-9+8-4x-2x = (2x+6x-4x-2x)+(-9+8) = 2x-1$$ 