SOLUTION: I need to simplify '2/3(12/4+2+3x)'. What I did first was divide 12 by 4 (3) then add 2 (5), leaving the 3x alone for now. Then I multiplied 5 by 2/3 getting 10/3 as my answer

Algebra ->  Expressions -> SOLUTION: I need to simplify '2/3(12/4+2+3x)'. What I did first was divide 12 by 4 (3) then add 2 (5), leaving the 3x alone for now. Then I multiplied 5 by 2/3 getting 10/3 as my answer      Log On


   

Question 1027515: I need to simplify '2/3(12/4+2+3x)'.
What I did first was divide 12 by 4 (3) then add 2 (5), leaving the 3x alone for now. Then I multiplied 5 by 2/3 getting 10/3 as my answer. But then I doubled checked by doing Distributive property. I mutiplied 12,4, and 2 by 2/3 and then did the problem (8 / 8/3 + 4/3). Doing that I kept getting 13/3.
So I am very confused now is the answer 10/3 or 13/3? Was I not allowed to use distributive property?
Found 2 solutions by josgarithmetic, addingup:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2/3(12/4+2+3x)

Best to clarify as %282%2F3%29%2812%2F4%2B2%2B3x%29

Work first inside the parentheses, for the factor on the right.
%282%2F3%29%283%2B2%2B3x%29

%282%2F3%29%285%2B3x%29
From here, the direction to NOT use Distributive Property is wrong. USE IT!

10%2F3%2B%282%2F3%29%283x%29

10%2F3%2B2x, but if you want one consolidated rational expression, USE the lowest common denominator of 3.
10%2F3%2B6x%2F3
%2810%2B6x%29%2F3

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
You say you need to simplify. Just simplify, not solve for x:
2/3(12/4+2+3x) = 2/3(3x+5)