Question

select the two expressions that are equal to 1/3 (9m + 18 ).

A. 3(m + 2)

C. 3( 1 + 2m)

B. 3+6m

D. 3m + 18

E. 3m + 6

F. 3 (m + 6)

Answer 1

To determine which expressions are equal to \( \frac{1}{3}(9m + 18) \), we first need to simplify \( \frac{1}{3}(9m + 18) \).

1. Distribute \( \frac{1}{3} \) to both terms inside the parentheses:

\[
\frac{1}{3}(9m + 18) = \frac{1}{3} \cdot 9m + \frac{1}{3} \cdot 18 = 3m + 6
\]

Now we need to find the expressions among the options that are equal to \( 3m + 6 \):

- **A.** \( 3(m + 2) = 3m + 6 \) (Equal)

- **B.** \( 3 + 6m \) (Not equal, this simplifies to \( 6m + 3 \))

- **C.** \( 3(1 + 2m) = 3 + 6m \) (Not equal, same as B)

- **D.** \( 3m + 18 \) (Not equal)

- **E.** \( 3m + 6 \) (Equal)

- **F.** \( 3(m + 6) = 3m + 18 \) (Not equal)

Based on the simplifications, the two expressions that are equal to \( \frac{1}{3}(9m + 18) \) are:

**A.** \( 3(m + 2) \)
**E.** \( 3m + 6 \)