ASRJC Inequalities Assignment Q1
ASRJC Inequalities Assignment Q1
10 marks
Tutorial
Solve the inequality \(\frac{8-5x}{2x+1}\le 2-x\). [4][4]
Deduce the set of values of \(x\) for which
- \(\frac{8-5\left| x \right|}{2\left| x \right|+1}\le 2-\left| x \right|\).[3]
- \(\frac{8-5\sin x}{2\sin x+1}\le 2-\sin x\), where \(0 < x < 2\pi \).[3]
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Answer:\(Main: \(\left\{x \in \mathbb{R} : x < -\frac{1}{2} \text{ or}\hspace{0.5em} 1 \leq x \leq 3\right\}\); (i) \(\left\{x \in \mathbb{R} : -3 \leq x \leq -1 \text{ or}\hspace{0.5em} 1 \leq x \leq 3\right\}\); (ii) \(\left\{x \in \mathbb{R} : x = \frac{\pi}{2} \text{ or}\hspace{0.5em} \frac{7\pi}{6} < x < \frac{11\pi}{6}\right\}\)
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