Question

Substitute w = 1 and w = 3 to determine if the two expressions are equivalent.

4 (3 w + 4) 16 w + 12

Which statements are true? Check all that apply.
The value of both expressions when w = 1 is 28.
The two expressions are equivalent.
The value of both expressions when w = 1 is 16.
The two expressions are not equivalent.
The value of both expressions when w = 3 is 52.
The value of both expressions when w = 3 is 60.

Answer 1

To determine if the two expressions \( 4(3w + 4) \) and \( 16w + 12 \) are equivalent, we can substitute the values \( w = 1 \) and \( w = 3 \) into both expressions and compare their outputs.

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

**First expression:**
\[
4(3(1) + 4) = 4(3 + 4) = 4 \times 7 = 28
\]

**Second expression:**
\[
16(1) + 12 = 16 + 12 = 28
\]

### Step 2: Evaluate both expressions at \( w = 3 \)

**First expression:**
\[
4(3(3) + 4) = 4(9 + 4) = 4 \times 13 = 52
\]

**Second expression:**
\[
16(3) + 12 = 48 + 12 = 60
\]

### Summary of Results

1. When \( w = 1 \):
- Value of both expressions: 28
2. When \( w = 3 \):
- Value of the first expression: 52
- Value of the second expression: 60

### Conclusion

- The value of both expressions when \( w = 1 \) is **28**.
- The two expressions are **not equivalent** because they yield different results when \( w = 3 \) (52 vs. 60).

### True Statements

- The value of both expressions when \( w = 1 \) is 28. (True)
- The two expressions are equivalent. (False)
- The value of both expressions when \( w = 1 \) is 16. (False)
- The two expressions are not equivalent. (True)
- The value of both expressions when \( w = 3 \) is 52. (True)
- The value of both expressions when \( w = 3 \) is 60. (False)

### Therefore, the true statements are:
- The value of both expressions when \( w = 1 \) is 28.
- The two expressions are not equivalent.
- The value of both expressions when \( w = 3 \) is 52.