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

To determine if the expressions \( 3v + 2(v + 1) - 4 \) and \( 16 + 3v - v \) are equivalent, we will evaluate both expressions at \( v = 3 \) and \( v = 6 \).

**First Expression:**
\[
3v + 2(v + 1) - 4
\]
**Second Expression:**
\[
16 + 3v - v
\]

### Step 1: Evaluate both expressions at \( v = 3 \)

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

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

### Step 2: Evaluate both expressions at \( v = 6 \)

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

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

### Summary of Results:
- When \( v = 3 \):
- First Expression: \( 13 \)
- Second Expression: \( 22 \)

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

### Conclusion:
From the evaluations:
- The value of both expressions when \( v = 3 \) is **not the same** (13 and 22).
- The value of both expressions when \( v = 6 \) is the same (28 and 28).

Thus, the true statements are:
1. The value of both expressions when \( v = 3 \) is 13. (True)
2. The value of both expressions when \( v = 6 \) is 28. (True)
3. The expressions are not equivalent. (True)

So the selected options are:
- The value of both expressions when \( v = 3 \) is 13.
- The value of both expressions when \( v = 6 \) is 28.

The expressions are **not equivalent**.