Understanding Linear Inequalities and Their Applications

This page introduces the fundamental concepts of linear inequalities and their graphical representations. The content explains how linear inequalities differ from linear equations and provides essential rules for solving them.

Definition: Linear inequalities are mathematical expressions that show the relationship between quantities that are not equal, using symbols like >, <, ≥, or ≤.

Highlight: When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.

Example: When graphing inequalities, use solid lines for ≤ or ≥, and dashed lines for < or >. For expressions like y > mx + b, shade the region above the line, while for y < mx + b, shade below the line.

Vocabulary: System of inequalities refers to multiple inequalities that must be solved simultaneously, with the solution being the region where all inequalities are satisfied.