1. **State the problem:** Given the equation $$\frac{1}{3}x - 6 = 10$$, prove that $$x = 48$$. 2. **Show the formula and rules:** To solve for $$x$$, we use the Multiplication Property of Equality, which states that multiplying both sides of an equation by the same nonzero number keeps the equation balanced. 3. **Step-by-step solution:** 1) Given: $$\frac{1}{3}x - 6 = 10$$ 2) Multiply both sides by 3 (Multiplication Property): $$3\left(\frac{1}{3}x - 6\right) = 3(10)$$ 3) Simplify right side: $$3\left(\frac{1}{3}x - 6\right) = 30$$ 4) Apply distributive property: $$3 \cdot \frac{1}{3}x - 3 \cdot 6 = 30$$ 5) Simplify multiplication: $$\cancel{3} \cdot \frac{1}{\cancel{3}} x - 18 = 30$$ which simplifies to $$x - 18 = 30$$ 6) Add 18 to both sides (Addition Property): $$x - 18 + 18 = 30 + 18$$ 7) Simplify: $$x = 48$$ 4. **Answer to the question:** The algebraic reason that justifies the transition from statement 1 to statement 2 is the **Multiplication Property** of Equality. This property allows us to multiply both sides of the equation by the same number (in this case, 3) to eliminate the fraction and simplify solving for $$x$$.