Without using a calculator, solve the inequality $\frac{x+6}{{{x}^{2}}-3x-4}\le \frac{1}{4-x}$. [3]

Question

Without using a calculator, solve the inequality $\frac{x+6}{{{x}^{2}}-3x-4}\le \frac{1}{4-x}$. [3] Hence, deduce the range of values of $x$ that satisfies $\frac{\left| x \right|+6}{{{x}^{2}}-3\left| x \right|-4}\le \frac{1}{4-\left| x \right|}$. [2] Solve the inequality $\ln \left( x+6 \right)\le -\frac{x}{3}$. [3]

Accepted Answer

(a) (i) $x\le -3.5$ 	ext{ or } $-1 < x < 4$ (ii) $-4 < x < 4$ (b) $-6 < x \le -3.15$

2013 CJC Promo Q8

2013 CJC Promo Q8

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