Given that $a\in \mathbb{R}$ and $a1$, use an algebraic method to solve the inequality

Question

Given that $a\in \mathbb{R}$ and $a>1$, use an algebraic method to solve the inequality $\frac{ax-a+2}{\left( x-a \right)\left( 1-x \right)}\le 1$.[5] Hence find the set of values of $x$ such that $\frac{a\left| x \right|-a+2}{\left( \left| x \right|-a \right)\left( 1-\left| x \right| \right)}\le 1$.[2]

Accepted Answer

(i) $x a$ (ii) $-1 a$ or $x<-a$

2023 VJC Promo Q3

2023 VJC Promo Q3

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