# Compound Inequalities

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## Objective

SWBAT solve a compound inequality and write their solution in interval notation.

#### Big Idea

Students will make connections between a solution graphed on a number line and written in interval notation.

## Launch

10 minutes

In this lesson launch (solving_inequalities_compound_launch), students will work by themselves for the first 3 minutes to try to develop a plan of how to find values that will make the given inequalities true (MP1).  After students have had time to consider a method of solution, they should talk to their partner to develop a plan together (MP3).  When students share out their responses, focus on one question at at time.

When looking at the first inequality, you can use the following prompts:

1) What are some of the values that will make this inequality true?

2) What is the smallest value of x that will make the inequality true?

3) If x=4, will the inequality still be true?  What about x=3.999?

4) Can you name an interval that will make the inequality true?

5) Can you represent this solution graphically?

For the second inequality, the following prompts may be helpful:

1) How is this inequality different from the first?

2) Look at each inequality separately.  What values will make each true?

3) The the values converging or diverging? (you may need to define these terms or use others).

4) Can you represent the solution to this inequality graphically?

## Independent Practice

25 minutes

This segment of the lesson (solving_inequalities_compound) will give students an opportunity to practice strategies for solving compound inequalities with their partner.  While students are working, encourage them to check values from their solution intervals in the original inequality (MP6).  It is helpful to have a copy of the answer key for this practice posted somewhere in the room so that students can check their work as they go.

## Closure

5 minutes

This ticket out the door (solving_inequalities_compound_close) requires students to not only solve the compound inequality but also to explain their solution (MP3).  Incorporating this writing component will help deepen a student's mastery of the skill while simultaneously helping them to better understand the concepts used in his/her response.  Encourage students to use mathematical vocabulary when explaining their solution.  If you have some key vocabulary words such as "inequality", "solution", "interval", etc. have them posted on the board so that students can purposely utilize them in their explanation.