# Ch 3: Common Core HS Algebra: Linear Inequalities

Explore our lessons on high school algebra. These lessons meet the Common Core Mathematics standards for linear inequalities (CCSS.Math.Content.HSA-CED.A.1; CCSS.Math.Content.HSA-CED.A.2; CCSS.Math.Content.HSA-REI.B.3; CCSS.Math.Content.HSA-REI.D.12).

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)

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.

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