What does it mean when the circles are open or closed? Where is the graph shaded?
x≤ 4 or x> 6
Practice makes perfect
Let's first look at where the shaded portion of the graph is. When a number line is shaded with an un-shaded section between two points, it represents an orcompound inequality. This is because the value of the variable must be greater than (or greater than or equal to) the greater point or less than (or less than or equal to) the lesser point.
Let's call the variable this compound inequality represents x and consider what inequalities could describe its value.
Lesser Point
The graph is shaded to the left of 4 and the circle is closed. This portion tells us that x is less than or equal to 4.
x≤ 4
Greater Point
The graph is also shaded to the right of 6 and the circle is open. This portion tells us that x is greater than 6.
x> 6
Compound Inequality
Notice that the graph of this compound inequality is split by an un-shaded region. This tells us that we have an or compound inequality. The solution set has no region of overlap, so either x is less than or equal to 4 or x is greater than 6.
x≤ 4 or x> 6
