Question

5/3-2/x=8/x?

if x was not equal to 0

Answer 1

`x=6`

Explanation:

`5/3-2/x=8/x|color(blue)(*x)`
`5/3color(blue)(*x)-2/cancel(x)cancel(color(blue)(*x))=8/cancel(x)cancel(color(blue)(*x))`
`5/3x-2=8|color(blue)(+2)`
`5/3xcancel(-2color(blue)(+2))=8color(blue)(+2)`
`5/3x=10|color(blue)(*3/5)`
`cancel(5/3color(blue)(*3/5))*x=2cancel(10)color(blue)(*3/cancel(5))`
`x=6`

Answer 2

`x=6`

Explanation:

First, ensure that all terms with `x` in the denominator are on the same side. This entails adding `2/x` to each side:

`5/3cancel(-2/x+2/x)=8/x+2/x`

Since the terms on the right have a common denominator, we can add:

`5/3=(8+2)/x`

`5/3=10/x`

Multiply each term by the term diagonal to it:

`5x=10(3)`

`5x=30`

Divide each side by `5:`

`(cancel5x)/cancel5=30/5`

`x=6`

Answer 3

`5/3-2/x=8/x`

`5/3cancel(-2/x)cancel(+2/x)=8/x+2/x`

`5/3=10/x`

`5/3*x=10/cancelx*cancelx` `->` `5/3x=10`

`cancel(5/3)x*cancel(3/5)=10*3/5`

`x=6`

Hope that helped!
~Chandler Dowd