Graphing Solutions

Inequality solutions are shown on a number line using specific notation. An open circle at 7 means x is greater than 7 (7 not included). A filled circle means x is greater than or equal to 7 (7 is included). The ray extends in the direction of valid values, giving you a visual picture of every number that satisfies the condition.

In two dimensions, inequalities define regions. y > 2x + 1 is every point above the line y = 2x + 1. Shading that region on a graph shows the solution set. Linear programming — used by airlines, logistics companies, and manufacturers — optimizes within these shaded regions.