1) Draw a

**number line**. 2) Put either an**open**circle or a**closed dot**above the**number**given. For ≤ and ≥ , use a**closed dot**to indicate the**number**itself is part of the solution. For < and >, use an**open**circle to indicate the**number**itself is not part of the solution.Similarly one may ask, how do you know whether to use an open circle or closed circle when graphing an inequality?

Here are some tips for

**graphing inequalities**on a number line.**Use an open circle**to show that a value is not a solution for the**inequality**. You will**use open circles**to**graph inequalities**that include the symbols >or <.**Use**a**closed circle**to show that a value is a solution for the**inequality**.What is the difference between a closed dot and an open dot?

A

**closed**(solid)**dot means**the endpoint is included in the curve and an**open dot means**it isn't. It's like the difference between "less than or equal to" and "less than". In the graph you show, both**dots**are**open**which**means**the function doesn't have any value, so isn't defined, at x_0.Is a closed circle a bracket or parenthesis?

Interval notation uses

**brackets**[ ] to show the closed**circles**; the numbers in the**parentheses**represent the ends of the shaded area. On the number line, there is a closed**circle**at a and the number line is shaded to the left.