Question

Identify the pair of equivalent expressions.(1 point)
Responses

2x+2
and 2(x+2)
2 x plus 2 and 2 times open paren x plus 2 close paren

3x+2x
and x2(3+2)
3 x plus 2 x and x squared times open paren 3 plus 2 close paren

−3(x+2)
and −3x−3
negative 3 times open paren x plus 2 close paren and negative 3 x minus 3

2(x+3)
and 2x+6
2 times open paren x plus 3 close paren and 2 x plus 6

Answer 1

To identify which pair of expressions are equivalent, we can simplify each pair:

1. **2x + 2** and **2(x + 2)**:
- \( 2(x + 2) = 2x + 4 \) (not equivalent to \( 2x + 2 \))

2. **3x + 2x** and **x²(3 + 2)**:
- \( 3x + 2x = 5x \)
- \( x²(3 + 2) = x² \cdot 5 = 5x² \) (not equivalent to \( 5x \))

3. **−3(x + 2)** and **−3x − 3**:
- \( −3(x + 2) = -3x - 6 \) (not equivalent to \( -3x - 3 \))

4. **2(x + 3)** and **2x + 6**:
- \( 2(x + 3) = 2x + 6 \) (these are equivalent)

Thus, the pair of equivalent expressions is:

**2(x + 3) and 2x + 6**.