Inequalities

CHAPTER 9

9.1 Linear Inequalities

When multiplying/dividing by a negative number, reverse the inequality sign!

E.g.: $-2x > 6$ → $x < -3$

9.2 Quadratic Inequalities

Inequality	Solution (if $\alpha < \beta$)
$(x-\alpha)(x-\beta) > 0$	$x < \alpha$ or $x > \beta$
$(x-\alpha)(x-\beta) < 0$	$\alpha < x < \beta$

"Greater than → take the outer regions; Less than → take the inner region"

Example

$(x-2)(x-3) < 0$

Less than → inner region: $2 < x < 3$

9.3 Compound Inequalities

Type	Solution
AND	Take intersection
OR	Take union

📘 MathsKiller Textbook Series | Chapter 9: Inequalities