Question

Are the expressions equivalent? Use j = 3 and j = 8 to determine if they are.

7(j – 2) 4j – 5

No, because when j = 8, the values of the expressions are different.
Yes, because when j = 3, the value of both expressions is 7 and when j = 8, the value of both expressions is 42.
Yes, because when j = 3, the value of both expressions is 7.
Yes, because when j = 8, the values of the expressions are different.

Answer 1

To determine if the expressions \( 7(j - 2) \) and \( 4j - 5 \) are equivalent, we can evaluate them for \( j = 3 \) and \( j = 8 \).

1. **For \( j = 3 \)**:
- **First expression**:
\[
7(3 - 2) = 7(1) = 7
\]
- **Second expression**:
\[
4(3) - 5 = 12 - 5 = 7
\]

So, for \( j = 3 \), both expressions yield 7.

2. **For \( j = 8 \)**:
- **First expression**:
\[
7(8 - 2) = 7(6) = 42
\]
- **Second expression**:
\[
4(8) - 5 = 32 - 5 = 27
\]

So, for \( j = 8 \), the first expression is 42 while the second expression is 27.

Since the values of the expressions are the same for \( j = 3 \) but different for \( j = 8 \), the expressions are not equivalent.

Thus, the correct response is:
**No, because when j = 8, the values of the expressions are different.**