Two Variable Equations and Inequalities

Lesson 17 Two Variable Linear Inequalities

TEKS 2A.3F and 3G

We will solve two variable linear inequalities.

I will summarize how to graphically solve and check solutions of two variable linear inequalities.

Poll

BELLRINGER- Solve the following Absolute Value Inequality:

$$\left|2x-4\right|\le6$$

Solution(s) is/are :

• $$-1\le x\le5$$  

• $$x\le-1\ or\ x\ge5$$

• $$x\le5$$

• $$x\ge-1$$

Review:

Dropdown

The symbol > means the line will be ​ ​

Select answer

and the shading will be ​

Select answer

the line.

Dropdown

The symbol $$\le$$ means the line will be ​

Select answer

and the shading will be ​

Select answer

the line.

Slope tells us where to shade

Using the slope-intercept form of an equation (y=mx+b) we can determine where to shade based off the slope!

​How to remember which slope is positive or negative on the graph:
Positive slope always starts in Quadrant I (+,+)
Negative slope always starts in Quadrant II (-,+)

Multiple Choice

Pick the graph below that displays a NEGATIVE linear slope.

Isolate the variable to one side of the inequality. Direction of the inequality determines where to shade!

​Only x: shade left (</≤) or shade right (>/≥)
Only y: shade below (</≤) or shade above (>/≥)

Special Cases:

Dropdown

If you have, for example, $$x>0$$ as your inequality, you would sketch the graph with a ​

Select answer

line and shade​

Select answer

of the line.