Question

Which expression is equivalent to − 2 3 ( 12 x + 3 y ) − 4 ( 7 x + 7 ) ? A. (8x – 2y) – (28x – 28) B. 2(18x – y – 14) C. –20x – y – 28 D. –2(18x + y + 14)

Answer 1

Answer: B and D.

Explanation:

To simplify the given expression, distribute the coefficients outside the parentheses:

- (2/3) * (12x + 3y) - 4 * (7x + 7)

Distributing the coefficients:

= -8x - 2y - 28x - 28

Combining like terms:

= -36x - 2y - 28

Now, let's compare this simplified expression with the given choices:

A. (8x - 2y) - (28x - 28)

- This simplifies to -20x + 26, not equivalent.

B. 2(18x - y - 14)

- This simplifies to 36x - 2y - 28, which is equivalent.

C. -20x - y - 28

- This is already simplified and is equivalent.

D. -2(18x + y + 14)

- This simplifies to -36x - 2y - 28, which is equivalent.

Therefore, the equivalent expression is found in both options B and D.