Graphing , , and on a Number Line
To graph each inequality on a number line, identify the boundary value, choose the correct endpoint symbol, and shade in the appropriate direction:
- : The solution set contains every number that is or less. Shade all values to the left of and place a bracket (or closed circle) at to show that itself is included in the solution set.
- : The solution set contains every number less than , but not itself. Shade all values to the left of and place an open parenthesis (or open circle) at to indicate that the endpoint is excluded.
- : The solution set contains every number greater than , but not itself. Shade all values to the right of and place an open parenthesis (or open circle) at to show it is excluded.
These three cases illustrate the two key decisions in graphing any single-variable inequality: the direction of shading (left for or , right for or ) and the endpoint symbol (bracket or closed circle when the endpoint is included; parenthesis or open circle when it is not).
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Ch.2 Solving Linear Equations and Inequalities - Elementary Algebra @ OpenStax
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Graphing , , and on a Number Line
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