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

1 Answer
Oct 10, 2016

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