How can I find the values of x here

Sorry...I should have been a little more explicit...we have

2 ≥  1/x^2     multiply both sides by x^2

2x^2 ≥ 1       divide both sides by 2

x^2 ≥ 1/2      subtract 1/2 from both sides

x^2 - 1/2 ≥ 0

Does that help ??

Does this help:

Let 1 - 1/x² = -1 and solve for x to get the limiting values of x at the -1 level

.

First be aware that x cannot equal 0

Next muliply everything by x squared

can you do it from there?

can you do it step by step ? 

Hi 315

it's after 3am here and I'm on my phone so my full answer will have to wait till morning.  Sorry  :)

no problem , thank you 

Let's take this in "pieces"

We have

-1 ≤ 1 - 1/x^2  subtract 1 from both sides

-2 ≤ -1/x^2     multiply both sides by -1 and reverse the inequality sign

2 ≥  1/x^2       rearrange

x^2 ≥ 1/2     subtract 1/2 from both sides

x^2 - 1/2 ≥ 0   factor

(x - 1/√2) (x + 1/√2) ≥ 0

And we have two possible intervals that work, here

(-∞, -1/√2] and [1/√2, ∞)

Now, let's look at the other piece

1 - 1/x^2 ≤ 1     subtract 1 from both sides

-1/x^2 ≤ 0         divide by -1 on both sides and reverse the sign

1/x^2 ≥ 0

And the possible intervals here are

(-∞, 0), (0, ∞)

But, we have to take the most "restrictive" intervals that would make the original inequality true

Notice that the interval (-1/√2, 1/√2) makes the original inequality untrue

So, the intervals that "work" are   (-∞, -1/√2] and [1/√2, ∞)

I dont understand this 

x^2 ≥ 1/2     subtract 1/2 from both sides

Thank you CPhill

now its very clear