1. The problem is to differentiate between the expressions "Multiply n by two, then add three" and "Add three to n, then multiply by two". 2. Let's translate each phrase into algebraic expressions: - "Multiply n by two, then add three" means first multiply $n$ by 2, then add 3: $$2n + 3$$ - "Add three to n, then multiply by two" means first add 3 to $n$, then multiply the result by 2: $$2(n + 3)$$ 3. Important rule: The order of operations matters. Multiplication and addition are not commutative in this context because the grouping changes the result. 4. Let's expand and simplify the second expression to see the difference: $$2(n + 3) = 2 \times n + 2 \times 3 = 2n + 6$$ 5. Comparing the two expressions: - First expression: $$2n + 3$$ - Second expression: $$2n + 6$$ 6. The difference is in the constant term: adding 3 after multiplying by 2 versus adding 3 before multiplying by 2 results in adding 3 versus adding 6. 7. To summarize: - "Multiply n by two, then add three" corresponds to $$2n + 3$$. - "Add three to n, then multiply by two" corresponds to $$2(n + 3) = 2n + 6$$. Final answer: The expressions are $$2n + 3$$ and $$2(n + 3)$$ respectively, which are not equal.