Question

How do you solve `4/x+7=6/x`?

Answer 1

The solution is `x=2/7`.

Explanation:

Multiply everything by `x` to get rid of the `x` in the denominator:

`4/x+7=6/x`

`4/xcolor(blue)(*x)+7color(blue)(*x)=6/xcolor(blue)(*x)`

`4/color(red)cancelcolor(black)xcolor(blue)(*color(red)cancelcolor(blue)x)+7color(blue)(*x)=6/color(red)cancelcolor(black)xcolor(blue)(*color(red)cancelcolor(blue)x)`

`4+7color(blue)(*x)=6`

`4+7x=6`

`4+7xcolor(blue)-color(blue)4=6color(blue)-color(blue)4`

`color(red)cancelcolor(black)4+7xcolor(red)cancelcolor(black)(color(blue)-color(blue)4)=6color(blue)-color(blue)4`

`7x=6color(blue)-color(blue)4`

`7x=2`

`color(blue)(color(black)(7x)/7)=color(blue)(color(black)2/7)`

`color(blue)(color(black)(color(red)cancelcolor(black)7x)/color(red)cancelcolor(blue)7)=color(blue)(color(black)2/7)`

`x=color(blue)(color(black)2/7)`

That's the solution. Hope this helped!

Answer 2

`2/7`

Explanation:

`4/x +7=6/x`

`rArr 4/x - 6/x=-7`

`rArr (4-6)/x = -7`

`rArr -2/x =-7`

`rArr x=2/7`

Hope this helps :)