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.