Question

Which expressions are equivalent to 2 (three-fourths x + 7) minus 3 (one-half x minus 5)? Check all that apply.
-1
29
2 (three-fourths x + 7) + (negative 3) left-bracket one-half x + (negative 5) right-bracket
2 (three-fourths x) + 2 (7) + 3 (one-half x) + 3 (negative 5)
2 (three-fourths x) + 2 (7) + (negative 3) (one-half x) + (negative 3) (negative 5)
A B C D E

Answer 1

Original: 2(3/4 x + 7) − 3(1/2 x − 5).

Distribute: 2·(3/4 x) + 2·7 − 3·(1/2 x) + 3·5 = 3/2 x + 14 − 3/2 x + 15 = 29.

So the equivalent expressions are:
- B (29),
- C: 2(3/4 x + 7) + (−3)(1/2 x + (−5)) which is the same as 2(... ) − 3(...),
- E: 2(3/4 x) + 2(7) + (−3)(1/2 x) + (−3)(−5), which simplifies to 29.

A (−1) and D simplify to different values, so they are not equivalent.