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−12negative 4 times open paren x minus 3 close paren is equal to negative 4 x minus 124x+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, let's simplify each option.

1. **Option 1:** \(-4x - 12 = -4(x + 3)\)

Simplifying the right side:
\[
-4(x + 3) = -4x - 12
\]
This equality holds:
\[-4x - 12 = -4x - 12\]
So these expressions are equivalent.

2. **Option 2:** \(-4(x - 3) = -4x - 12\)

Simplifying the left side:
\[
-4(x - 3) = -4x + 12
\]
This does not match with \(-4x - 12\):
\[-4x + 12 \neq -4x - 12\]
Not equivalent.

3. **Option 3:** \(4x + 12 = -4(x - 3)\)

Simplifying the right side:
\[
-4(x - 3) = -4x + 12
\]
Again, this does not match:
\[4x + 12 \neq -4x + 12\]
Not equivalent.

4. **Option 4:** \(-4(x + 3) = 4x - 12\)

Simplifying the left side:
\[
-4(x + 3) = -4x - 12
\]
This does not match \(4x - 12\):
\[-4x - 12 \neq 4x - 12\]
Not equivalent.

From the evaluation above, the only pair that shows equivalent expressions is:

**Option 1:** \(-4x - 12 = -4(x + 3)\)