Ask a New Question
Menu

Which pair shows equivalent expressions?(1 point)

Responses

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

−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

1 answer

To find which pair shows equivalent expressions, we can simplify each equation.

  1. 4x + 12 = -4(x - 3)

    • Distributing -4:
    • \( 4x + 12 = -4x + 12 \)
    • Now, add \( 4x \) to both sides:
    • \( 8x + 12 = 12 \), which simplifies down to \( 8x = 0 \) or \( x = 0 \).

  2. -4x - 12 = -4(x + 3)

    • Distributing -4:
    • \( -4x - 12 = -4x - 12 \)
    • This is actually the same expression on both sides, so they are equivalent.

  3. -4(x + 3) = 4x - 12

    • Distributing -4:
    • \( -4x - 12 = 4x - 12 \)
    • Adding \( 4x \) to both sides gives \( -12 = 8x - 12 \), which is not equivalent.

  4. -4(x - 3) = -4x - 12

    • Distributing -4:
    • \( -4x + 12 = -4x - 12 \)
    • This simplifies to \( 12 = -12 \), which is not equivalent.

Thus, the pair that shows equivalent expressions is: −4x−12=−4(x+3).