# Common Core HS Algebra: Linear Inequalities

## About this chapter

**Standard:** Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (CCSS.Math.Content.HSA-CED.A.1)

**Standard:** Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (CCSS.Math.Content.HSA-CED.A.2)

**Standard:** Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (CCSS.Math.Content.HSA-REI.B.3)

**Standard:** Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (CCSS.Math.Content.HSA-REI.D.12)

## About This Chapter

Students who have mastered these standards are able to work out and graphically solve various types of inequalities. When discussing these concepts, they will be able to identify and define the different inequality representations.

Lessons in this standard cover concepts such as:

- Graphing 1- and 2-variable inequalities
- Working with set notation, compound inequalities and systems of inequalities
- Solving and graphing absolute value inequalities

Students demonstrate the mastery of this standard when creating expressions that describe relationships or numbers. Mastery of these standards can support students through their education and career when they need to solve some math problems that have more than one solution.

### How to Use These Lessons in Your Classroom

Here are some tips for how to use the lessons to support instruction in these standards:

#### Solving Linear Inequalities Lessons

Create a worksheet and show your students the video lessons regarding how to solve inequalities. In addition to passing out the worksheets, require your students to team up with one other student to complete the worksheet. Spend time at the end of the class having the groups come up and work out the inequalities in front of everyone.

#### Graphing Inequalities Lessons

Develop a worksheet that consists of different types of inequalities. Have the students watch all video lessons about graphing inequalities. Provide your students with graphing paper and the worksheet. Give your students time to graph the inequalities. Display the correct graphs on an overhead projector and explain the answers.

#### Compound Inequalities and Systems of Inequalities Lessons

Exhibit the video lesson 'Set Notation, Compound Inequalities and Systems of Inequalities.' Write various types of compound inequalities and systems of inequalities on the board. Call on students to identify the different examples and explain their answers.

Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!

Linear inequalities may look intimidating, but they're really not much different than linear equations. In this lesson, we'll practice solving a variety of linear inequalities.

So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!

It's good to know that inequalities can help you say things like 'I'm happy when the temperature is above 60 degrees.' But sometimes it's good to be more specific and say something like 'I'm happy when it's between 60 and 90 degrees.' Learn how this relates to a system of inequalities here!

If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.

Taking two skills and combining them to make a more complicated problem is a classic tactic in mathematics. If you feel confident with absolute values and inequalities, see if you can tackle them with their powers combined here!

Solving and graphing absolute value inequalities brings a lot of different skills together in one place. The practice problems in this video will give you a good chance to see more examples of absolute value inequalities but will also test your general algebraic knowledge.

**Watched all the videos in this chapter?**