Find the region of the inequality by graphing the line of the corresponding equation. Replace the inequality symbol with an equal sign to find the boundary of the region. Now you will need to find out which side of the line is the region you are interested in. Pick a point that is clearly on one side of the line. You should choose a point that is easy to calculate with. The origin (0, 0) is often a good choice. If this point fits into the original inequality, the side with the chosen point on it is the region of the inequality. If the chosen point does not work, the other side of the line is the region of the graph of the inequality.
Decide if the points on the boundary line are part of the region of the inequality. If the inequality sign is either "less than or equal to" or "greater than or equal to," the points on the boundary line are part of the region. If the inequality sign is either "less than" or "greater than," the points on the boundary line are not part of the region.
Deal with inequalities where the variable has an exponent, such as "X^2 is less than 5," by graphing all of the solutions. When a point is chosen to determine the region, you will either be selecting everything to the leftmost solution line or everything to the right of the leftmost solution line. For functions like "Cos X is less than 0," you may have an infinity of solution lines, so the entire graph is the inequality region.