Question

Which of the following pairs of algebraic expressions are equivalent?(1 point)
Responses

6d+4−3d
and 3(d−13)+5

6 d plus 4 minus 3 d and 3 left parenthesis d minus Start Fraction 1 over 3 End Fraction right parenthesis plus 5

11r+2(r+4)
and 11r+4(r+2)

11 r plus 2 left parenthesis r plus 4 right parenthesis and 11 r plus 4 left parenthesis r plus 2 right parenthesis

4h+12−2h
and −5h+10+3h+2

4 h plus 12 minus 2 h and negative 5 h plus 10 plus 3 h plus 2

(5t−3)+2t
and (3t−2)+5t

Answer 1

Only the first pair is equivalent.

Work:
- 6d + 4 − 3d = 3d + 4.
3(d − 1/3) + 5 = 3d − 1 + 5 = 3d + 4. => equivalent.

- 11r + 2(r + 4) = 11r + 2r + 8 = 13r + 8.
11r + 4(r + 2) = 11r + 4r + 8 = 15r + 8. => not equivalent.

- 4h + 12 − 2h = 2h + 12.
−5h + 10 + 3h + 2 = −2h + 12. => not equivalent.

- (5t − 3) + 2t = 7t − 3.
(3t − 2) + 5t = 8t − 2. => not equivalent.