2023 HCI Promo Q1
2023 HCI Promo Q1
5 marks
Promo
Without using a calculator, solve the inequality \({\frac{4{{x}^{2}}+6x-12}{2x-1}\le 3}\).[3]
Deduce the solution of the inequality \({\frac{4{{\mathrm{e}}^{2x}}+6{{\mathrm{e}}^{x}}-12}{2{{\mathrm{e}}^{x}}-1}\le 3}\) in exact form.[2]
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Answer:\(x \leq -\frac{3}{2}\) or \(\frac{1}{2} < x \leq \frac{3}{2}\); \(\ln\frac{1}{2} < x \leq \ln\frac{3}{2}\)
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