How Do You Graph Inequalities on a Number Line?

Graphing inequalities on a number line requires you to shade the entirety of the number line containing the points that satisfy the inequality. Make a shaded or open circle depending on whether the inequality includes the value.

  1. Solve the inequality

    For example with the inequality 3x + 6 >= 15, isolate x as its own term. Subtract 6 from both sides, leaving 3x >= 9, then divide by 3 on both sides. The value of x should be greater than or equal to 3.

  2. Draw the number line

    Set a value for zero, and mark the increments as necessary. Mark arrows on either end of the line to denote that the line is understood to extend further. Mark the spot on the line that corresponds to the value of x you just found. In this case, it’s 3, so make a mark at that point. If the inequality includes the value, shade the number. If it’s simply greater than or less than, circle the point.

  3. Shade the number line

    If the value for x is less than the value you plotted on the number line, shade everything to the left of the point. If it’s greater, shade everything to the right.