1. **State the problem:** Solve for $x$ in the equation $\frac{a(x-2)}{2} = 5$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the denominator to eliminate the fraction. 3. **Step-by-step solution:** Multiply both sides by 2: $$2 \times \frac{a(x-2)}{2} = 5 \times 2$$ Simplifies to: $$a(x-2) = 10$$ Divide both sides by $a$ (assuming $a \neq 0$): $$\frac{a(x-2)}{\cancel{a}} = \frac{10}{\cancel{a}}$$ $$x-2 = \frac{10}{a}$$ Add 2 to both sides: $$x - 2 + 2 = \frac{10}{a} + 2$$ $$x = \frac{10}{a} + 2$$ 4. **Final answer:** $$x = \frac{10}{a} + 2$$ This method applies similarly to the other equations by multiplying both sides by the denominator, then isolating $x$.