Question

How do you solve `(x-2)/x<(x-4)/(x-6)`?

Answer 1

The solution of the inequality is `x < 3`.

Explanation:

This inequality is solved by first cross multiplying, then solving the inequality.

`(x - 2)/x < (x - 4)/(x - 6)`
`(x - 2)(x - 6) < x(x - 4)`
`x^2 - 6x - 2x + 12 < x^2 - 4x`
`x^2 - 8x + 12 < x^2 - 4x`
`x^2 -x^2 - 8x + 12 < x^2 - x^2 - 4x`
`-8x + 12 < -4x`
`-8x + 4x + 12 < -4x + 4x`
`-4x + 12 < 0`
`-4x + 12 - 12 < 0 - 12`
`-4x < -12`
`(-4x)/-4 < (-12)/-4`
`x < 3`