Question

What is the solution set of [1/x-2]<-2

Answer 1

Answer:

  3/2 < x < 2

Step-by-step explanation:

We assume the problem is ...

  [tek]\dfrac{1}{x-2}<-2[/tex]

This will not be true for x-2 > 0 because that would make the left side positive. So, we must have x < 2, which makes the denominator negative. Multiplying by (x-2), we get ...

  1 > -2(x -2)

  1 > -2x +4

  2x > 3 . . . . . . add 2x-1

  x > 3/2

From above, we also have x < 2, so the solution set is ...

  3/2 < x < 2