Question

How do you solve `7/(9x)+2/3=5+1/(3x)`?

Answer 1

`x=4/39`

Explanation:

to clear the denominators, multiply both sides by `9x`

`(9x)(7/(9x)) = 7`;
`(9x)(2/3) = 6x`;
`(9x)(5) = 45x`;
`(9x)(1/(3x))=3`

you now have `7+6x=45x+3`

by subtracting `6x` and 3 from both sides, you get `39x=4`

divide both sides by 39

`x=4/39`

Answer 2

Multiply the equation by numbers that will eliminate the denominator terms.

Explanation:

In this case we would multiply the whole thing by 9x because that is the least value that includes factors from all of the denominators (x, 3, 9).
`(9*x)*(7/(9*x) + 2/3 = 5 + 1/(3*x))`

`7 + 6*x = 45*x + 3` ; Now we can solve for ‘x’ normally.

`4 = 39*x` ; `x = 0.103`

CHECK:
`7/(9*0.103) + 2/3 = 5 + 1/(3*0.103)`
`7/0.927 + 2/3 = 5 + 1/0.309`

`7.55 + 0.667 = 5 + 3.24`
`8.22 = 8.24` OK, given rounding errors.