### Graphs of Inequalities in One Variable

A **linear inequality** in two variables takes the form

When we graph a line in the coordinate plane, we can see that it divides the plane in half:

The solution to a linear inequality includes all the points in one half of the plane. We can tell which half by looking at the inequality sign:

> The solution set is the half plane above the line.

< The solution set is the half plane below the line.

For a strict inequality, we draw a **dashed line** to show that the points in the line *are not* part of the solution. For an inequality that includes the equals sign, we draw a **solid line** to show that the points on the line *are* part of the solution.

#### Solution Sets

This is a graph of

This is a graph of

**Graph Linear Inequalities in One Variable in the Coordinate Plane**

In the last few sections we graphed inequalities in one variable on the number line. We can also graph inequalities in one variable on the coordinate plane. We just need to remember that when we graph an equation of the type

#### Graphing Inequalities

1. Graph the inequality

First let’s remember what the solution to

The solution to this inequality is the set of all real numbers

In two dimensions, the solution still consists of all the points to the right of

The line

2. Graph the inequality

The absolute value inequality

In other words, the solution is all the coordinate points for which the value of **and** smaller than 5. The solution is represented by the plane between the horizontal lines

Both horizontal lines are dashed because points on the lines are not included in the solution.

### Example

#### Example 1

Graph the inequality

The absolute value inequality

In other words, the solution is all the coordinate points for which the value of **or** greater than or equal to 2. The solution is represented by the plane to the left of the vertical line

Both vertical lines are solid because points on the lines are included in the solution.

### Review

Graph the following inequalities on the coordinate plane.

x<20 y≥−5 x>0.5 x≤12 y>−23 y<−0.2 |x|>10 |y|≤7 |y|<13 |x|≥−10

### Review (Answers)

To view the Review answers, open this PDF file and look for section 6.11.

### Texas Instruments Resources

*In the CK-12 Texas Instruments Algebra I FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9616.*