Graphing inequalities is the process of showing what part of the number line contains values that will "satisfy" the given inequality.
Examine the first inequality x > -5. A graph of this inequality will show what numbers may be used to replace x in our inequality to make a true statement. Notice that the circle above -5 is not shaded in because a possible solution does NOT include -5. An arrow is drawn to the right of -5 to show that all values greater than -5 may be used for x.
The second inequality reads that x must be greater than OR equal to 8. Therefore we must start at 8 and include 8 as a possible solution by darkening in the circle above. The arrow must be drawn to the right to show that all values on the number line greater than 8 are possible solutions.
The third inequality states that x must be less than -6. The circle drawn above -6 must NOT be shaded in because -6 is NOT a possible solution for x. An arrow moving to the left of -6 should be shown. This is where values are less than -6.
The fourth inequality states that x must be less than OR equal to 12. The circle above 12 will be shaded in to include 12 as a possible solution. The arrow will be pointing to the left of 12 because this is where values on the number line are less than 12.