1. **State the problem:** Solve the equation $$4(x - 5) = 25$$ for $$x$$ using two strategies. 2. **Strategy A: Use the Distributive Property** - Apply the distributive property: $$4(x - 5) = 4 \times x - 4 \times 5 = 4x - 20$$ - Rewrite the equation: $$4x - 20 = 25$$ 3. **Isolate the variable term** - Add 20 to both sides to cancel the $$-20$$: $$4x - 20 + 20 = 25 + 20$$ $$4x = 45$$ 4. **Isolate the variable** - Divide both sides by 4: $$\frac{4x}{\cancel{4}} = \frac{45}{\cancel{4}}$$ $$x = \frac{45}{4}$$ 5. **Strategy B: Divide out a common factor first** - Divide both sides of the original equation by 4: $$\frac{4(x - 5)}{\cancel{4}} = \frac{25}{\cancel{4}}$$ $$x - 5 = \frac{25}{4}$$ 6. **Isolate the variable** - Add 5 to both sides: $$x - 5 + 5 = \frac{25}{4} + 5$$ $$x = \frac{25}{4} + \frac{20}{4} = \frac{45}{4}$$ **Final answer:** $$x = \frac{45}{4}$$