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## Operations and Algebraic Thinking 218-221

### Course: Operations and Algebraic Thinking 218-221>Unit 5

Lesson 7: Intro to inequalities with variables

# Graphing inequalities review

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, space, start underline, is less than, end underline, space, a, plus, 2
x, is less than, 5

### Inequalities symbols

SymbolMeaning
is greater thanGreater than
start underline, is greater than, end underlineGreater than or equal to
is less thanLess than
start underline, is less than, end underlineLess than or equal to

## Graphing inequalities with variables

We can use a number line to show the possible solutions to an inequality.
Example 1: x, is greater than, 4
An inequality like x, is greater than, 4 tells us that x can be any 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, space, start underline, is less than, end underline, space, 3
If we have either the start underline, is greater than, end underline or start underline, is less than, end underline symbol in our inequality, we shade in the circle to show that the variable may be equal to that number.
For example, y, space, start underline, is less than, end underline, space, 3 is graphed as follows:
This number line shows that y is either equal to 3 or less than 3.