Question

Darren and Quincy wanted to justify that the expression One-sixth (6 x + 12) minus one-half (4 x + 2) is equivalent to Negative x + 1. Their justifications are shown below. Darren’s Method: Substitute 2 into both expressions One-sixth (6 x + 12) minus one-half (4 x + 2) = one-sixth (6 (2) + 12) minus one-half (4 (2) + 2) = one-sixth (24) minus one-half (10) = negative 1. negative x + 1 = (negative 2) + 1 = negative 1 Quincy’s Method: Substitute 6 into both expressions One-sixth (6 x + 12) minus one-half (4 x + 2) = one-sixth (6 (6) + 12) minus one-half (4 (6) + 2) = one-sixth (48) minus one-half (26) = negative 5. negative x + 1 = (negative 6) + 1 = negative 5 Which explains who is correct? Only Darren is correct because he substituted x = 2 into the expressions. Only Quincy is correct because he substituted a number that is the same as the denominator of one of the fractions. Both are correct because after substituting the same value into both expressions, the result is the same. Both are correct because after submitting different values into each expression, the result is the same.

Answer 1

Answer:

c: Both are correct because after substituting the same value into both expressions, the result is the same.

Step-by-step explanation:

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Answer 2

Answer:

Both are correct because after substituting the same value into both expressions, the result is the same.

Step-by-step explanation:

Given the expression:

(1/6)*(6*x + 12) - (1/2)*(4*x + 2)

Applying distributive property:

(1/6)*6*x + (1/6)*12 - (1/2)*4*x - (1/2)*2 =

= x + 2 - 2x - 1 =

= -x + 1

Then, for any number substituted into both equations, the result is the same