Question

Solve the inequality 1/(2-X) < 1

Answer 1

1 < 2-X
-1 < -X
x < 1

Answer 2

yea i shoulda wrote it out

Answer 3

you are going to have to start with
\[\frac{1}{2-x}-1<0\] and go from there

Answer 4

@jimmyrep you cannot multiply by 2 - x because you don't know whether it is positive or negative

Answer 5

Okay Thanks!

Answer 6

it is true that
\[x<1\] is a solution, but so is
\[x>2\]

Answer 7

you get
\[\frac{x-1}{2-x}<0\] and check on the intervals
\[(-\infty, 1), (1,2),(2, \infty)\] and see that first and third work

Answer 8

i agree with what you said - you are right - its not valid to multiply by 2-x

Answer 9

checking on the intervals is valid