1. **State the problem:** Match each sentence to its corresponding equation. 2. **Analyze each sentence and equation:** - Sentence 1: "3 times the difference between a number and 3 is equal to 15." - The difference between a number and 3 is written as $(y - 3)$. - "3 times" means multiply by 3: $3(y - 3)$. - Equal to 15: $3(y - 3) = 15$. - Sentence 2: "The difference between 3 times a number and 3 is equal to 15." - 3 times a number: $3w$. - Difference between $3w$ and 3: $3w - 3$. - Equal to 15: $3w - 3 = 15$. - Sentence 3: "The difference between 2 times the square of a number and 3 is equal to 1." - Square of a number: $x^2$. - 2 times the square: $2x^2$. - Difference between $2x^2$ and 3: $2x^2 - 3$. - Equal to 1: $2x^2 - 3 = 1$. - Sentence 4: "The difference between the square of twice a number and 3 is equal to 1." - Twice a number: $2z$. - Square of twice a number: $(2z)^2$. - Difference between $(2z)^2$ and 3: $(2z)^2 - 3$. - Equal to 1: $(2z)^2 - 3 = 1$. 3. **Final matching:** - Sentence 1 matches equation: $3(y - 3) = 15$ - Sentence 2 matches equation: $3w - 3 = 15$ - Sentence 3 matches equation: $2x^2 - 3 = 1$ - Sentence 4 matches equation: $(2z)^2 - 3 = 1$