1. **State the problem:** Given the equation $$\frac{1}{4}x + 5 = 7$$, prove that $$x = 8$$. 2. **Review the given proof steps:** | Statement | Reason | |---|---| | 1) $$\frac{1}{4}x + 5 = 7$$ | Given | | 2) $$4\left(\frac{1}{4}x + 5\right) = 4(7)$$ | Multiplication Property | | 3) $$4\left(\frac{1}{4}x + 5\right) = 28$$ | Arithmetic | | 4) $$x + 20 = 28$$ | Distributive Property | | 5) $$x = 8$$ | Subtraction Property | 3. **Focus on the transition from statement 3 to statement 4:** - Statement 3 is $$4\left(\frac{1}{4}x + 5\right) = 28$$. - Statement 4 is $$x + 20 = 28$$. 4. **Explain the algebraic reason for this step:** - The expression $$4\left(\frac{1}{4}x + 5\right)$$ is expanded using the **Distributive Property**, which states: $$a(b + c) = ab + ac$$ - Applying this here: $$4 \times \frac{1}{4}x + 4 \times 5 = x + 20$$ - This shows the multiplication distributes over addition inside the parentheses. 5. **Conclusion:** The algebraic reason justifying the transition from statement 3 to statement 4 is the **Distributive Property**. **Final answer:** Distributive Property