Question

How do you solve `(x+6)/x=10/7`?

Answer 1

`x=14`

Explanation:

In solving an equation where one fraction is equal to another fraction we can use the method of `color(blue)"cross-multiplication"`

`rArrcolor(blue)(x+6)/color(red)(x)=color(red)(10)/color(blue)(7)`

Now multiply the `color(red)"red terms"` together, the `color(blue)"blue terms"` together and equate them.

`rArrcolor(red)(10x)=color(blue)(7(x+6))`

distribute the bracket.

`rArr10x=7x+42`

subtract 7x from both sides of the equation.

`10x-7x=cancel(7x)cancel(-7x)+42`

`rArr3x=42`

To solve for x, divide both sides by 3

`(cancel(3) x)/cancel(3)=42/3`

`rArrx=14" is the solution"`

`color(blue)"As a check"`

substitute x = 14 into the equation and if the left side equals the right side then x = 14 is the solution.

`"left side " =(14+6)/14=20/14=10/7=" right side"`