What does it mean when the circles are open or closed? Where is the graph shaded?
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Practice makes perfect
Let's first look at where the shaded portion of the graph is. When a number line is shaded with a shaded section between two points, it represents an andcompound inequality. This is because the value of the variable must be greater than (or greater than or equal to) the lesser point and less than (or less than or equal to) the greater 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 right of -3 and the circle is open. This portion tells us that x is greater than -3.
x> -3
Greater Point
The graph is also shaded to the left of 2 and the circle is open. This portion tells us that x is less than 2.
x< 2
Compound Inequality
Notice that a number line is shaded with a shaded section between two points. This tells us that we have an and compound inequality. The solution set is a region of overlap, so x is bothgreater than -3 and less than 2.
First Inequality: - 3< x&
Second Inequality: x& < 2
Compound Inequality: - 3< x& < 2
