Question

How do you solve `1/3x+2/9=5/6x+1/2`?

Answer 1

Transfer `5/6 x "and" 2/9`
`x/3-(5x)/6=1/2-2/9`
LCM on LHS and on RHS too
`(2x)/6-(10x)/6=9/18-4/18`
`(-8x)/6=5/18`
Transfer 6
`-8x=5/cancel18^3xxcancel6`
Transfer -8
`x=5/3 div -8`
`x=5/3xx1/(-8)`
`x=-5/24`

Answer 2

`x=-30/54`

Explanation:

1/

`1/3 x+2/9 = 5/6 x +1/2`

2/

`2/9-1/2 = 5/6 x -1/3 x`

3/

`4/18-9/18 = 5/6 x -2/6 x`

4/

`-5/18 = 3/6 x`

5/

`-30/54 = x`

Thus, `x=-30/54`