We are asked to compare the graphs of a compound inequalities involving and and or. Note that there are infinitely many solutions for this exercise. We are only illustrating one an example of each type. However, all of the graphs of each type will follow the same pattern, for the most part.
Graphing an AND inequality
The graph of a compound inequality with the word and contains the overlap of the individual inequalities that form the compound inequality. For example, let's graph the following compound inequality.
All real numbers that are greater than -2
and less than4.
We can start by graphing the first inequality: all real numbers that are greater than -2.
Now, we can graph the second inequality: all real numbers that are less than 4.
The graph of the compound inequality contains the overlapping region of the individual ones.
Graphing an OR inequality
The graph of a compound inequality with the word or contains both graphs of the individual inequalities that form the compound inequality. For example, let's graph the following compound inequality.
All real numbers that are less than-2
or greater than4.
We can start by graphing the first inequality: all real numbers that are less than -2.
Now, we can graph the second inequality: all real numbers that are greater than 4.
The graph of the compound inequality contains each region of the individual ones.
Comparison and conclusions
Let's look at the graphs of both compound inequalities at the same time.
We describe the difference between the two types of graphs by saying that graphs of compound inequalities using and contain the intersection of individual inequalities, while compound inequalities using or contain the union of individual inequalities.
