Question

Use v = 3 and v = 6 to determine if the expressions 3v + 2(v + 1) – 4 and 16 + 3v – v are equivalent. Which statements are true? Select two options.
The value of both expressions when v = 3 is 13.
The value of both expressions when v = 3 is 22.
The value of both expressions when v = 6 is 28.
The value of both expressions when v = 6 is 46.
The expressions are equivalent.
The expressions are not equivalent.

Answer 1

Let's evaluate the expressions \( 3v + 2(v + 1) - 4 \) and \( 16 + 3v - v \) for both \( v = 3 \) and \( v = 6 \).

1. **For \( v = 3 \)**:

- **First Expression**:
\[
3v + 2(v + 1) - 4 = 3(3) + 2(3 + 1) - 4
\]
\[
= 9 + 2(4) - 4 = 9 + 8 - 4 = 9 + 4 = 13
\]

- **Second Expression**:
\[
16 + 3v - v = 16 + 3(3) - 3
\]
\[
= 16 + 9 - 3 = 16 + 6 = 22
\]

2. **For \( v = 6 \)**:

- **First Expression**:
\[
3v + 2(v + 1) - 4 = 3(6) + 2(6 + 1) - 4
\]
\[
= 18 + 2(7) - 4 = 18 + 14 - 4 = 18 + 10 = 28
\]

- **Second Expression**:
\[
16 + 3v - v = 16 + 3(6) - 6
\]
\[
= 16 + 18 - 6 = 16 + 12 = 28
\]

Now we can summarize our results:
- For \( v = 3 \):
- **First Expression**: 13
- **Second Expression**: 22

- For \( v = 6 \):
- **First Expression**: 28
- **Second Expression**: 28

Now let's evaluate the statements:

1. The value of both expressions when \( v = 3 \) is 13. **(False)**
2. The value of both expressions when \( v = 3 \) is 22. **(True - only the second expression)**
3. The value of both expressions when \( v = 6 \) is 28. **(True - both expressions)**
4. The value of both expressions when \( v = 6 \) is 46. **(False)**
5. The expressions are equivalent. **(False)**
6. The expressions are not equivalent. **(True)**

**Selected Options**:
- The value of both expressions when \( v = 6 \) is 28.
- The expressions are not equivalent.