Question

Zoe, Latoya, Christina, and Rhoda each used a different method to verify that Negative 2 (3 x minus 12) = negative 6 x + 24.


Zoe
Latoya
Christina
Rhoda
Step 1
Substitute opposite values of x into both expressions.
Substitute the same value of x into both expressions. Substitute opposite values of x into both expressions. Substitute the same value of x into both expressions.
Step 2
The
expressions are equivalent if the values of the expressions are equal.
The expressions are equivalent if the value of one of the expressions is zero. The expressions are equivalent if the values of the expressions are opposites.
The expressions are equivalent if the values of the expressions are equal.

Whose method can be used to verify that the distributive property was correctly applied to the expression?
Zoe’s method
Latoya’s method
Christina’s method
Rhoda’s method

Answer 1

Rhoda’s method.

Explanation: Substitute the same value of x into both expressions and check they give the same result.
Example: x = 0: -2(3·0 − 12) = -2(−12) = 24 and -6·0 + 24 = 24.
x = 1: -2(3·1 − 12) = -2(−9) = 18 and -6·1 + 24 = 18.
Since the values match, the distributive step is correct (and algebraically −2(3x − 12) = −6x + 24).