# How do i go about solving this? |2x−1| > √(1−x^2)

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I have tried spiting to 2x−1 > √(1−x^2) and 2x−1 < -√(1−x^2) and solving for x, but the second part does not work out, or at least i cant figure it out

I have tried spiting to 2x−1 > √(1−x^2) and 2x−1 < -√(1−x^2) and solving for x, but the second part does not work out, or at least i cant figure it out

##### 1 Answer

#### Explanation:

and

For the first inequality, let's first solve the equation:

Square both sides:

move everything to one side:

So

Since the inequality is only valid on

So consider the intervals

So far our solution set is

Now let's look at the second inequality.

First we'll solve the equality for the intersection points:

square both sides:

moving everything to one side:

so the intersections are

Since this inequality is only valid on

So consider the intervals

Overall the solution set is