✦ MA Intelligence →
Math Academy SG
You are here: Home / Questions / Inequalities: NJC 2024 Promo Q1

by

Inequalities: NJC 2024 Promo Q1

National Junior College2024 PromoPromo Q1●○○ Foundational4 marks

What this question tests

Solving inequalities.

Question

Without using a calculator, solve the inequality x+3x2+x−2≥−1.\frac{x+3}{x^2+x-2} \geq -1. [4]

Show full worked solution▾

(Inequality)

Suggested Solution

x+3x2+x−2≥−1x+3x2+x−2+x2+x−2x2+x−2≥0x2+x−2+x+3x2+x−2≥0x2+2x+1x2+x−2≥0(x+1)2(x−1)(x+2)≥0.\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<−2orx>1orx=−1.x<-2\quad\text{or}\quad x>1\quad\text{or}\quad x=-1.

Answers

x<−2x < -2 or x>1x > 1 or x=−1x = -1

← All Inequalities questionsJC H2 Maths tuition at Math Academy