Without using a calculator, solve the inequality $\frac{5x-1}{{{x}^{2}}+x-6}\le 1$. [3] Hence solv

Question

Without using a calculator, solve the inequality $\frac{5x-1}{{{x}^{2}}+x-6}\le 1$. [3] Hence solve $1+\frac{1-5\ln x}{{{\left( \ln x \right)}^{2}}+\ln x-6}\ge 0$. [2]

Accepted Answer

(i) $x < -3$, $-1 \le x < 2$, or $x \ge 5$ (ii) $0 < x < \mathrm{e}^{-3}$, $\mathrm{e}^{-1} \le x < \mathrm{e}^2$, or $x \ge \mathrm{e}^5$

2013 YJC P1 Q4

2013 YJC P1 Q4

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