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

Question

6034 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-27T14:31:49

#0 > - 1#

#x/(x - 1) < 1#

Cross multiply!

#x/(x - 1) < 1/1#

#x xx 1 < (x - 1) xx 1#

#x < x - 1#

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

#0 > - 1#

Answer 2 · 2017-10-27T15:03:50

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

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

First, pass everything to the left of your inequality:

#x/(x-1)<1#

#x/(x-1)<(x-1)/(x-1)#

#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#