1/(1+x^2) < 1/2

TIA

To solve the inequality 1/(1+x^2) < 1/2, we can start by multiplying both sides of the inequality by the positive number 2 to avoid changing the direction of the inequality.

2 * 1/(1+x^2) < 1

Next, we can simplify the left side of the inequality by multiplying the numerator and denominator by 2:

2/(1+x^2) < 1

Now, if we cross-multiply and distribute, we get:

2 < 1 + x^2

Subtracting 1 from both sides gives:

1 < x^2

Now, taking the square root of both sides, remembering to consider both the positive and negative square roots:

±√1 < x

Which simplifies to:

-1 < x < 1

Therefore, the solution to the inequality 1/(1+x^2) < 1/2 is -1 < x < 1.