Question

Question #f5060

Answer 1

`x>= 3` or `x<2`

Explanation:

We begin with the inequality:

`1/(x-2) <= 1`

It would seem reasonable to take the reciprocal of both sides of this equation, and we need to remember that doing so reverses the direction of the inequality. In addition, later we need to check in the original inequality that we don't create a zero in the denominator:

`x-2 >= 1`

We can now add 2 to both sides:

`x>= 3`

Finally, we can see that we don't create a zero in the denominator which would require that `x=2`, so we don't need to add any restrictions to this part of our solution.

Next we need to consider where the answer can be negative since negative values are less than `1`. This happens when

`x<2`

Therefore, we have the solution that

`x>= 3` or `x<2`

A quick graph of the equation and limit in the y-axis helps us confirm that we have the correct answer.