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TUTORIALS:
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Graphing Solutions of Inequalities
Solving an inequality means describing a set, not just finding
a number. This set is the solution set of the
problem. To visualize the solution set, draw it on the number
line. To do this, draw the number line and shade the part of the
number line corresponding to the solution set. The solution set
to a single inequality will be a half line that may or may not
include the endpoint. When the endpoint is included, draw a solid
dot for the endpoint. When the endpoint is not included, draw a
circle.
Example 1
Represent the solution set of x  5 on a number line.
Solution
The solution set of x 5 is represented by the set of points to the left of
5 on the number line. It does include the endpoint, since x = 5
is included.
Example 2
Represent the solution set of x > 2 on a number line.
Solution
The solution set of x > 2 is a half line represented by the
set of points to the right of 2 on the number line. It does not
include the endpoint, since x = 2 is not included.
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