Question

How do you solve `\frac { x - 8} { x } = \frac { 2} { 5}`?

Answer 1

Multiply both sides by `x xx 5` to remove the denominators. and then solve for x

Explanation:

`x xx 5 xx ( x-8) /x = x xx 5 xx (2)/ 5` This results in

`5 ( x -8) = x xx2` multiplying across the parenthesis

`5x - 40 = 2x`

Move the x's to left side of the equation and the -40 to the left side of the equation.

`5x -2x - 40 + 40 = 2x -2x +40` which gives

`3x = +40` Divide both sides by 3

`3x/3 = 40/3` Which gives

`x = 13 1/3`

Answer 2

`x = 40/3`

Explanation:

Cross multiply the two fractions, and go from there.

`5(x-8) = 2x`

`5x - 40 = 2x`

Isolate the x by putting like terms on the same side.

`3x - 40 = 0`

`3x = 40`

`x = 40/3`

Answer 3

`x=40/3`

Explanation:

Solve:

`(x-8)/color(red)x=2/color(blue)5`

Cross multiply the denominators.

`color(blue)5(x-8)=2xxcolor(red)x`

Simplify `2xxcolor(red)x` to `2x`.

`5(x-8)=2x`

Expand the left-hand side.

`5x-40=2x`

Add `40` to both sides.

`5x=2x+40`

Subtract `2)x` from both sides.

`5x-2x=40`

Simplify.

`3x=40`

Divide both sides by `3`.

`x=40/3`