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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

1 answer

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).