Review graphing inequalities with variables on number lines, and then try some practice problems.

Inequalities

Inequalities show the relation between two expressions that are not equal.
Below are some examples of inequalities:
9, is greater than, 7
6 < a+26\ \underline< \ a+2
x, is less than, 5

Inequalities symbols

SymbolMeaning
is greater thanGreater than
>\underline>Greater than or equal to
is less thanLess than
<\underline<Less than or equal to

Graphing inequalities with variables

We can use a number line to show the possible to solutions to an inequality.
Example 1: x, is greater than, 4
When we have an inequality like x, is greater than, 4, we do not know what x equals, but we know it is a value greater than 4.
We can show this on a number line by putting an open circle on 4 and shading the numbers that are greater than 4.
Example 2: y < 3y\ \underline<\ 3
If we have either the >\underline> or <\underline< symbol in our inequality, we shade in the circle to show that the variable may be equal to that number.
For example, y < 3y\ \underline<\ 3 is graphed as follows:
This number line show that y is either equal to 3 or less than 3.
Want to learn more about graphing inequalities? Check out this video.

Practice

Problem 1
Choose the inequality that represents the following graph.
Please choose from one of the following options.

Want to try more problems like this? Check out these exercises:
Inequality from graph
Plotting inequalities