
A complex inequality is two or more inequalities in a single statement. A complex inequality is a conjunction of two or more inequalities. This means that all the inequalities must be true at the same time. The complex inequality 2 < a ≤ 4 can also be written 2 < a and a ≤ 4. 
Step  Equation(s)  Description  Graph 

1  2 < a ≤ 3  This is the inequality to graph  
2  2 < a ≤ 3  Since 2 < a, 2 is not included in the inequality. Put a hollow dot at 2.  
3  2 < a ≤ 3  Since a ≤ 3, 3 is included in the inequality. Put a solid dot at 3.  
4  2 < a ≤ 3  The lefthand side of the inequality states that a member of the inequality must be greater than 2.  
5  2 < a ≤ 3  The righthand side of the inequality states that a member of the inequality must be less than or equal to 3.  
6  2 < a ≤ 3  Any point that is included in the inequality must be in both rays, so draw a line segment for the points included in both rays.  
7  2 < a ≤ 3  Remove the extra rays. 
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