Question

Which pair of expressions is equivalent?

a. 15a + 6 and 3(5a +3)
b. 14b +4 and 2(7b -2)
c. 5(2c +3) and 7c + 8d. 3(d + 5/3) and 3d + 5

Answer 1

`3(d+(5)/(3))=3d+5`

Explanation:

Two expression are called equivalent if after simplifying them we get same expression,

In option a :

By using distributive property,

3(5a + 3) = 3(5a) + 3(3) = 15a + 9 ≠ 15a + 6

In option b :

2(7b-2) = 2(7b) - 2(2) = 14b - 4 ≠ 14b + 4

In option c :

5(2c+3) = 5(2c) + 5(3) = 10c + 15 ≠ 7c + 8d,

In option d :

`3(d+(5)/(3))=3d+3* (5)/(3)=3d+5`

Hence, OPTION d has the pair of equivalent expression.

Answer 2

a. 15a+6 and 3(5a+3)
15a +6. not equivalent 15a +9


b. 14b +4. and 2(7b-2)
14b + 4. not equivalent 14b -4


c. 5(2c+3). and 7c+8d. 3(d+5/3) and 3d+ 5
10c + 15. and 7c+8d. 3d + 5. and 3d +5

I am assuming 3(d+5/3) and 3d+ 5 is a separate answer from c

so your answer would be 3(d+5/3) and 3d+ 5 are equivalent