ASRJC Inequalities Tutorial Q10

Find the range of values of \({x}\) for which \({\left| \frac{x}{2} + 3 \right| > 3 - x^{2}}\). [3]

Hence, solve

1. \({\left| \frac{e^{x}}{2} - 3 \right| > 3 - e^{2x}}\);[3]
2. \({\left| \frac{\sin x}{2} + 3 \right| < 2 + \cos^{2}x,\quad \mathrm{for } 0 < x < 2\pi}\).[3]