Page 2: Solving Inequalities with Absolute Value

This page delves into solving inequalities involving absolute values and their geometric interpretations on the number line, with particular focus on practical applications and visual representations.

Definition: For any positive real number a and expression w, |w| < a is equivalent to -a < w < a.

Example: When solving |x-2| < 3, the solution is x ∈ (-1,5), which can be visualized on a number line.

Highlight: When dividing an inequality by a negative number, both the inequality sign and the direction change.

Vocabulary: Równania i nierówności z wartością bezwzględną poziom rozszerzony zadania (Advanced level absolute value equations and inequalities exercises) require understanding of both algebraic and geometric approaches.

Quote: "Remember that when dividing by -1, change both the sign of the inequality and reverse its direction."