1. **State the problem:** Solve the equation $$2(x - 9) = 10$$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. This helps us expand expressions like $$2(x - 9)$$. 3. **Analyze Noah's method:** - Noah adds 9 to both sides directly after $$2(x - 9) = 10$$, which is incorrect because the 9 is inside the parentheses and not a separate term. - His step $$2(x - 9) + 9 = 10 + 9$$ is invalid. - Therefore, Noah's solution $$x = \frac{19}{2}$$ is incorrect. 4. **Analyze Elena's method:** - She correctly applies the distributive property: $$2(x - 9) = 2x - 18$$. - Then she subtracts 18 from both sides: $$2x - 18 - 18 = 10 - 18$$. - This step is incorrect because subtracting 18 twice on the left side is wrong. - The correct step should be subtracting 18 once: $$2x - 18 - (-18)$$ or simply adding 18. - So Elena's solution $$x = -4$$ is incorrect. 5. **Analyze Andre's method:** - He correctly applies the distributive property: $$2(x - 9) = 2x - 18$$. - Then he adds 18 to both sides: $$2x - 18 + 18 = 10 + 18$$, which is correct. - Simplifies to $$2x = 28$$. - Divides both sides by 2: $$\frac{2x}{2} = \frac{28}{2}$$, so $$x = 14$$. - Andre's method is correct. 6. **Final answer:** The correct solution is $$x = 14$$, found by Andre's method. **Summary:** Only Andre's method correctly solves the equation by properly applying the distributive property and performing valid operations on both sides of the equation.