The document explains the differences between linear inequalities and linear equations in two variables, highlighting that inequalities represent non-equivalence while equations indicate equivalence. It provides a step-by-step guide for graphing linear inequalities, which includes converting the inequality to an equation, plotting the graph with identified slope and y-intercept, determining the type of line (solid or broken), and shading the appropriate solution area. Multiple examples and repetition emphasize the consistent approach needed for graphing linear inequalities.