Section 8

Inequalities

fundamentalviz

a x + b > 0

It is solved by isolating the variable; dividing by a negative number reverses the inequality sign.

fundamentalviz

a x^{2} + b x + c > 0

It is solved using roots and sign analysis.

intermediateviz

\frac{P ( x )}{Q ( x )} > 0

The signs of the numerator and denominator are analyzed by intervals.

fundamentalviz

∣ x ∣ < a ⟺ - a < x < a; ∣ x ∣ > a ⟺ x < - a o x > a

Interprets absolute-value inequalities as distances.