1. We are asked to simplify the expression $$\frac{1}{4}(4x - 12) - \frac{1}{2}(4 - 10x)$$. 2. First, distribute the fractions over the terms inside the parentheses: $$\frac{1}{4} \times 4x - \frac{1}{4} \times 12 - \frac{1}{2} \times 4 + \frac{1}{2} \times 10x$$ 3. Calculate each multiplication: $$x - 3 - 2 + 5x$$ 4. Combine like terms: $$x + 5x - 3 - 2 = 6x - 5$$ 5. The simplified expression is: $$6x - 5$$