Help with Algebra Problem?

Question

The problem is z + 4 over 2 - z equals 13 over 5

I have to find if 1/3 is a solution for z, but I did:

(1/3 + 4) over (2 - 1/3)

(1/3 + 4/1) over (2/1 - 1/3)

(1/3 + 12/3) over (6/3 - 1/3)

(13/3) over (5/3)

Three's cancel out and I'm left with 13/5?

I have no clue??

Answer 1

Yes the threes cancel so you are right, 13/5 is the answer so 1/3 is a solution

Answer 2

Okay, so the key here is that you need to cross multiply.

Original problem:

(z+4) =      13/5

----------    

(2-z)                

        So then you cross multiply the denominator from one side of the equal sign with the numberator on the other side of the equal sign and vice versa such as:

5(z+4) = 13(2-z)   This removes any denominator from both sides.

Then you multiply the factors in the parentheses:

5z+20 = 26-13z

Bring the "z" variables together and move the non-variables to one side:

5z+13z = 26-20

18z = 6     Then you divide both sides by 18 which gives you:

z= 1/3