How Do You Graph the Union of Two Inequalities?

The "U" means "union"
The union of two inequalities is all the values for x that are in EITHER inequality
We have an open circle and a left-pointing arrow at 80 because x is less than 80
We have a closed circle and a right-pointing arrow at 105 because x is greater than or equal to 105
The union is everything that is covered by EITHER graph

1. Since 80 is one of the endpoints of our inequality, we put a circle there when we graph it
2. The circle is OPEN because we have a less than symbol
1. "x is less than 80" means that x is not included in the inequality
2. We represent this on a number line with an OPEN circle at 80
1. To determine this, we need to look at our inequality symbol
1. When we have a less than symbol, we have a left-pointing arrow
1. Since 105 is one of the endpoints of our inequality, we put a circle there when we graph it
2. The circle is CLOSED because we have a less than or equal to symbol
1. "x is greater than or equal to 105" means that x IS included in the inequality
2. We represent this on a number line with an CLOSED circle at 105
1. To determine this, we need to look at our inequality symbol
1. When we have a greater than or equal to symbol, we have a right-pointing arrow
1. The union is everything included in EITHER inequality
1. The union is just EVERYTHING that's already on the graph!
2. That was easy, right?

Graph the union of x<80 and x≥105 on a number line