Question

Which pair shows equivalent expressions?(1 point)
Responses

−4x−12=−4(x+3)
negative 4 x minus 12 is equal to negative 4 times open paren x plus 3 close paren

−4(x+3)=4x−12
negative 4 times open paren x plus 3 close paren is equal to 4 x minus 12

−4(x−3)=−4x−12
negative 4 times open paren x minus 3 close paren is equal to negative 4 x minus 12

4x+12=−4(x−3)

Answer 1

To determine which pair shows equivalent expressions, let’s simplify each expression one by one.

1. **First pair**: \(-4x-12 = -4(x+3)\)
- Right side: \(-4(x + 3) = -4x - 12\)
- This is equivalent.

2. **Second pair**: \(-4(x+3) = 4x-12\)
- Left side: \(-4(x + 3) = -4x - 12\)
- This is not equivalent since \(-4x - 12 \neq 4x - 12\).

3. **Third pair**: \(-4(x-3) = -4x-12\)
- Right side: \(-4(x - 3) = -4x + 12\)
- This is not equivalent since \(-4x + 12 \neq -4x - 12\).

4. **Fourth pair**: \(4x+12 = -4(x-3)\)
- Right side: \(-4(x - 3) = -4x + 12\)
- This is not equivalent since \(4x + 12 \neq -4x + 12\).

The equivalent expressions are found in the **first pair**:
\(-4x - 12 = -4(x + 3)\).