How to Graph Solutions to Inequalities on a Numberline

Create a dot on the number line at the given number when graphing a simple inequality, such as x ≤ 10. Draw the dot solid, or filled, if the inequality symbol includes an "equals to" or as an open circle if the symbol doesn't. Shade to the left of the dot for "less than" and to the right of the dot for "greater than." Draw an arrow at the end of the shading to indicate continuation as there are no terms given to define the end of the set.

Graph an intersecting compound inequality, such as 4 < x < 9, by first creating the solid or open dots at the numbers. Note that because "x" falls between the solution sets of 4 < x and x < 9, the section between the dots (open since the signs don't include "equals to") should be shaded in as the full, intersecting solution set.

Graph a compound inequality that doesn't intersect, such as x > 3 or x < -2, by first creating the appropriate type of circles on those numbers. Shade the solution sets separately, including the arrows, since the sets do not include one another. In this example, there would be an open circle on -2 with shading (and arrow) to its left and an open circle on 3 with shading (and arrow) to its right.