Without using a calculator Solve the inequality $\frac{2{{x}^{2}}+5x+9}{x-7}\le x-4$.[4] Hence, so

Question

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]

Accepted Answer

(i) $x\le -8-\sqrt{83}$ or $\sqrt{83}-8\le x<7$ (ii) $-\ln 7 < x \le -\ln \left( \sqrt{83}-8 \right)$

2019 NJC P1 Q2

2019 NJC P1 Q2

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