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N2026 P1 Q6

N2026 P1 Q6

Junior College 2
7 marks
  1. Solve the inequality \(\dfrac{2}{x+1} < 3-2x\).[4]
  2. Hence solve exactly the inequality \(\dfrac{2}{\sin\theta+1} < 3-2\sin\theta\), for \(0 < \theta < 2\pi\).[3]

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Answer:(a) \(x < -1\) or \(-\dfrac{1}{2} < x < 1\) (b) \(0 < \theta < \dfrac{\pi}{2}\) or \(\dfrac{\pi}{2} < \theta < \dfrac{7\pi}{6}\) or \(\dfrac{11\pi}{6} < \theta < 2\pi\)

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