2019 NJC P1 Q2
2019 NJC P1 Q2
6 marks
Prelims
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Without using a calculator
- Solve the inequality \(\frac{2{{x}^{2}}+5x+9}{x-7}\le x-4\).[4]
- Hence, solve the inequality \(\frac{2+5{{e}^{x}}+9{{e}^{2x}}}{7{{e}^{x}}-1}\ge 4{{e}^{x}}-1\).[2]
Video Solution:
Default solution
Correction to the intermediate logarithmic bound: multiplying \(\ln(\sqrt{83}-8)\le -x<\ln7\) by \(-1\) gives \(-\ln(\sqrt{83}-8)\ge x>-\ln7\). Retain the minus sign before \(\ln7\). The final interval shown has the correct sign.
Answer: (i) \(x\le -8-\sqrt{83}\) or \(\sqrt{83}-8\le x<7\) (ii) \(-\ln 7 < x \le -\ln \left( \sqrt{83}-8 \right)\)
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