Inequalities & Absolute Value

Instead of a single solution, inequalities give intervals: x > 3 means every number larger than 3. Graph them on a number line with open/closed dots for strict vs inclusive bounds.

Inequalities describe ranges

Instead of a single solution, inequalities give intervals: x > 3 means every number larger than 3. Graph them on a number line with open/closed dots for strict vs inclusive bounds.

Adding/subtracting the same number preserves the inequality direction.
Multiplying or dividing by a positive number preserves direction.
Multiplying or dividing by a negative number reverses the inequality.
Compound: a < x < b means x greater than a AND less than b.

Absolute value equations

|A| = k (k ≥ 0) means A = k or A = −k. Geometrically, points at distance k from the origin of A.