# Solve Inequalities Using Addition and Subtraction

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## Objective

SWBAT solve inequalities using addition and subtraction

#### Big Idea

Inequalities can be solved like equations. The meaning of the solution is different.

## Introduction

10 minutes

I will begin with the essential question:  How can we use addition and subtraction to solve inequalities?  I will explain that inequalities can be solved in the same manner as equations.  I may then ask students to discuss what is different about the solution to inequalities compared to equations.  We explored the meaning of inequalities solutions in the lesson Translating Verbal Statements Into Inequalities.

Next I will model an example while students copy what I do.  Each example is followed by a quick check for understanding problems labeled "You Try!".  For these problems, I sometimes have the students work on them by themselves.  At other times, when I think I need to energize the class, I will cold call students to provide the next step in the solution.

I think it is important to discuss the solutions with the class.  Using example 1, I may say some number x less 7 results in a value greater than 4.  What values of x can we take away 7 and end up with a difference greater than 4?  We know through the solution that x > 11.  I will call on students to try values of x that make the inequality true.  I think this helps reinforce what an inequality is and makes students exercise their abstract and quantitative reasoning (MP2).

I will ask students to graph their solutions on a number line.

## Guided Problem Solving

15 minutes

Students will not work on the 8 guided problem solving problems.  If I noticed a lot of students in the previous section making computation errors, I may need to change the approach to this section.  The main purpose of this lesson is for students to understand that they use an inverse operation to solve.  To check for students ability to do this, I will ask them only to write the first step of each inequality.  Using GP1 as an example, they would only need to show subtracting 7 on both sides of the inequality.  Students should be able to do this in a very short amount of time.

Once this is done for all 8 problems, they may solve and graph the solutions.

## Independent Problem Solving

20 minutes

Students now work independently.  The first 8 problems are very similar to the previous 8 problems.  Students should rely on those problems to help.  I will ask students to make sure they write the first step (the inverse operation step) on their papers explaining that it helps me to better understand their work.

Problem 9 asks students to explain the meaning of a solution to an equation vs an inequality.  I think it is important to repeatedly remind students that an equation has 1 solution and an inequality has many solutions.

The last 3 problems require students to write one-step inequalities from word problems.  Students may need to pull out their notes from the lesson Translating Verbal Statements Into Inequalities.  They will be able to use the graphic organizer to help choose the correct inequality symbol.

## Exit Ticket

5 minutes

Before beginning the exit ticket, I will ask students to discuss how to solve addition and subtraction inequalities.  Then students will take the exit ticket.

There are 5 questions on the exit ticket and each will be worth 1 point, including problem 5.  Students will earn 1 point for noting that the solutions of the given equation and inequality are different because in the equation m can only equal 3, whereas in the inequality m can be any value greater than 3.