Question

Identify the pair of equivalent expressions.

3x + 12 and 3 (x + 4)

-2 (x + 2) and -2 +4

3x + 4x and x^2 (3 + 4)

3 (x + 2) and 3x + 5

Answer 1

To identify the pair of equivalent expressions, we will simplify each option:

1. **3x + 12 and 3(x + 4)**
- Simplifying 3(x + 4):
\(3(x + 4) = 3x + 12\)
- These expressions are equivalent.

2. **-2(x + 2) and -2 + 4**
- Simplifying -2(x + 2):
\(-2(x + 2) = -2x - 4\)
- The second expression simplifies to 2.
- These expressions are not equivalent.

3. **3x + 4x and x^2(3 + 4)**
- Simplifying 3x + 4x:
\(3x + 4x = 7x\)
- Simplifying x^2(3 + 4):
\(x^2(3 + 4) = 7x^2\)
- These expressions are not equivalent.

4. **3(x + 2) and 3x + 5**
- Simplifying 3(x + 2):
\(3(x + 2) = 3x + 6\)
- These expressions are not equivalent.

The only pair of equivalent expressions is **3x + 12 and 3(x + 4)**.