Question

Are the expressions 3(m-2) + 2(m - 2) equivalent? Express your answer in 2 or more complete sentences.

A. Yes, they are equivalent because the coefficients of m are the same in both expressions.
B. No, they are not equivalent because they have different constant terms.
C. Yes, they are equivalent because they have the same variables and coefficients.
D. No, they are not equivalent because they have different variable terms.

Answer 1

The expressions 3(m-2) + 2(m - 2) are equivalent after distributing and combining like terms, which results in 5m - 10, confirming that they have the same variables and coefficients. The correct answer is C. Yes, they are equivalent because they have the same variables and coefficients.

Step-by-step explanation:

The expressions 3(m-2) + 2(m - 2) are equivalent. To determine this, we distribute the coefficients inside the parentheses and then combine like terms. For the first expression, we have 3 × m which is 3m, and 3 × (-2) which is -6. For the second expression, we have 2 × m which is 2m, and 2 × (-2) which is -4. Combining both, we get 3m - 6 + 2m - 4 which simplifies to 5m - 10. Since both terms involve the same variable m and the coefficients and constants can be combined consistently, the expressions are indeed equivalent. Therefore, the correct answer is C. Yes, they are equivalent because they have the same variables and coefficients.