Question

hich 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

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

−4(x−3)=−4x−12

Answer 1

To determine which pair shows equivalent expressions, we need to simplify or evaluate each option.

1. **First option:**
\(-4x - 12 = -4(x + 3)\)
Simplifying the right side:
\(-4(x + 3) = -4x - 12\)
So this option is true:
\(-4x - 12 = -4x - 12\)

2. **Second option:**
\(-4(x + 3) = 4x - 12\)
Simplifying the left side:
\(-4(x + 3) = -4x - 12\)
This leaves: \(-4x - 12 \neq 4x - 12\), so this option is false.

3. **Third option:**
\(4x + 12 = -4(x - 3)\)
Simplifying the right side:
\(-4(x - 3) = -4x + 12\)
This leaves: \(4x + 12 \neq -4x + 12\), so this option is false.

4. **Fourth option:**
\(-4(x - 3) = -4x - 12\)
Simplifying the left side:
\(-4(x - 3) = -4x + 12\)
This leaves: \(-4x + 12 \neq -4x - 12\), so this option is false.

Thus, the only equivalent expression is from the **first option**:
**−4x−12=−4(x+3)**.