Let's Review

You have learned that inequalities are mathematical statements that compare two numbers or quantities that are not equal. The symbols you can use to describe the relationship between the two numbers or quantities that are not equal are reviewed in the table below.

Symbol	Meaning
$\gt$	Greater than
$\lt$	Less than
$\geq$	Greater than or equal to
$\leq$	Less than or equal to
$\neq$	Not equal to

If an inequality contains a variable, then you can use a number line to create a visual reference to show all the values that make the inequality true. For example:

The steps for graphing inequalities on a number line are shown in the table below. Click each step to see it applied to the example.

Step 1: Plot the numeric value on the number line. Use an open circle if it is a strict inequality. Use a closed circle if it is non-strict inequality.	This is a non-strict inequality. 0 plotted on a number line with a closed circle.
Step 2: Shade the number line in the correct direction. If the variable is on the left-hand side of the inequality, then shade in the direction that the inequality points. If the variable is on the right-hand side of the inequality, then shade in the opposite direction of the inequality.	The variable is the on the right-hand side of the inequality. The inequality $0 \leq x$ on a number line.
Step 3: Check the shading by selecting any value in the shaded region and substituting it back into the inequality to make sure a true statement results.	Substitute $x = 1$ $0 \leq \left( 1 \right)$ $0 \leq 1$

Show your skills!

How well can you graph inequalities on a number line? Use the activity below to practice. Match the inequality on the left with its graph on the right.

$x \leq 2$

$2 \gt x$

$x \geq - 2$

$- 2 \lt x$

$2$ plotted on a number line with a closed circle. All numbers to the left of 2 are shaded.

$2$ plotted on a number line with an open circle. All numbers to the left of 2 are shaded.

$- 2$ plotted on a number line with an open circle. All numbers to the right of $-$2 are shaded.

$- 2$ plotted on a number line with a closed circle. All numbers to the right of $-$2 are shaded.

Directions To match items, click or tap an item in the left column and then click or tap its match in the right column. If you change your mind, make a different choice. Once you have matched all items, click "Check Answers" to see how you did. Click "Reset" to try again. Check Answers

Great job!

Reset