Once inequalities are solved (click here to go to a
lesson on solving one-step inequalities),
we can graph the solution set.

In the inequality x < 4, "x" could be any number less than 4. 

This not only includes integers, but decimals and fractions, too.  We can graph the solution set on a number line.

To graph our solution set we must show that all the numbers less than 4 (but not including the 4) could replace the "x" in x < 4. 

We show this by placing an open circle on the 4 and drawing an arrow to the left to show "less than".

Let's graph the solution set for the inequality x ≥ -1.

To graph this solution set we must show that all the numbers greater than -1, including the -1, could replace the "x". 

We show this by placing a closed circle on the -1 and drawing an arrow to the right to show "greater than".


Things to remember...

  If the symbol in the inequality is < or >, use an open circle above the number being graphed.

  If the symbol in the inequality is ≤ or ≥, use a closed circle above the number being graphed.

  If the symbol in the inequality is < or ≤, draw an arrow to the left to show "less than".

  If the symbol in the inequality is > or ≥, draw an arrow to the right to show "greater than".
 

Let's practice graphing inequalities.

 

 
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