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.