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Inequalities: NJC 2024 Promo Q1

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National Junior College2024 PromoPromo Q1●○○ Foundational4 marks

What this question tests

Solving inequalities.

Question

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

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(Inequality)

Suggested Solution

$\begin{aligned} \frac{x+3}{x^2+x-2}&\geq-1\\ \frac{x+3}{x^2+x-2}+\frac{x^2+x-2}{x^2+x-2}&\geq0\\ \frac{x^2+x-2+x+3}{x^2+x-2}&\geq0\\ \frac{x^2+2x+1}{x^2+x-2}&\geq0\\ \frac{(x+1)^2}{(x-1)(x+2)}&\geq0. \end{aligned}$ $x<-2\quad\text{or}\quad x>1\quad\text{or}\quad x=-1.$

Answers

$x < -2$ or $x > 1$ or $x = -1$

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