# How do you solve x/(x-1)<1?

Oct 27, 2017

$0 > - 1$

#### Explanation:

$\frac{x}{x - 1} < 1$

Cross multiply!

$\frac{x}{x - 1} < \frac{1}{1}$

$x \times 1 < \left(x - 1\right) \times 1$

$x < x - 1$

$x - x > - 1$, Note sign changes..

$0 > - 1$

Oct 27, 2017

Applying a standard procedure, the answer is $x < 1$.

#### Explanation:

We are dealing with polynomials and inequalities. The standard procedure is this:

First, pass everything to the left of your inequality:

$\frac{x}{x - 1} < 1$

$\frac{x}{x - 1} < \frac{x - 1}{x - 1}$

$\frac{1}{x - 1} < 0$

Then try to see when the expression at left is bigger or lower than zero:
Since 1 is always positive, this expression will be true when

$x - 1 < 0$

$x < 1$