Answer
$$ -\frac{3 \pi }{4} \lt x \lt \frac{\pi }{4}$$
Work Step by Step
We solve as follows:
$$-\frac{\pi }{2} \lt x+ \frac{\pi }{4} \lt \frac{\pi }{2} \quad \Rightarrow \quad \\ -\frac{\pi }{2} - \frac{\pi }{4} \lt x+ \frac{\pi }{4} - \frac{\pi }{4} \lt \frac{\pi }{2} - \frac{\pi }{4} \quad \Rightarrow \quad \\ -\frac{3 \pi }{4} \lt x \lt \frac{\pi }{4}$$
