SWBAT graph one variable inequalities.

How do we graph infinitely many solutions to an inequality?

10 minutes

Students will review the concept of translating inequalities.

**Do Now:**

1) Write as an inequality, using h as the height: All riders on the roller coaster must be at least 48 inches tall.

2) Write as an inequality, using a as the amount of money: Tommy is not sure how much money he has saved. He has greater than $10, but no more than $23.

The first problem is similar to expressions that students worked on in the previous lesson, Writing Algebraic Inequalities. The second problem adds a deeper level of understanding so I will ask students questions to help them with the translation.

*How is problem 2 different from problem 1?*

Students may notice that problem 2 refers to a range of values.

*Is there a minimum amount of money Tommy has saved? Is there a maximum?*

The phrase "greater than" indicates the minimum and "no more than" indicates the maximum.

*Can you write this as two inequalities?*

Students should be able to write the inequalities: a > 10 and a ≤ 23

*Can we combine these into one inequality?*

Students may have more difficulty with the compound inequality. 10 < a ≤ 23

10 minutes

Before students begin graphing inequalities, we will explore the meaning of an inequality and the solutions that make an inequality true.

*x = 3 has how many solutions?*

Students may think that it is a "trick" question, so I will clarify with follow up questions.

*Do we need to solve for x? Do we know what x is? Can x be 10 or any other number?*

Students should realize that for this equation, x can only be 3.

*x > 3 has how many solutions?*

Students may realize that for this inequality, x has a lot of solutions. For students who are confused, I will ask a few follow up questions.

*Can x be 3.1? 12? 4 billion?*

Students should understand that x is any number larger than 3.

*For this inequality, x has infinitely many solutions.*

I will explain to students that there is a way to show the solution to an inequality. We will formulate steps as we complete an example together.

**Example 1 - Graph x >3**

Step 1 - Draw a number line.

Step 2 - Draw a circle at the number in the inequality sentence.

*What number should we draw a circle at?*

Step 3 - If the symbol is < or >, leave the circle open.

If the symbol is ≥ or ≤, color in the circle completely.

*Should we close the circle or leave it open?*

Step 4 - Shade in the direction of the solution set.

*What is a possible value for x?*

We will continue with a few more examples. I will ask the same questions of students to help them through the steps of graphing. Examples 4 and 5 may be more difficulty for students, so I will ask additional questions.

**Example 2 - Graph x ≤ 1**

**Example 3 - Graph y < -4**

**Example 4 - Graph -5 < x ≤ 4**

*What is different about this inequality?*

Students should recognize that this is a compound inequality with a minimum and maximum value.

*What is the minimum? What is the maximum? How can we graph these on the number line?*

Similar to the steps of the previous examples, students may realize that we can use circles to indicate the minimum and maximum.

*What type of circles should we have at each number?*

An open circle should be place at -5 and a closed circle at 4.

*How can we indicate that the solution to this inequality is between these two numbers and not beyond them?*

We will shade only between the values.

**Example 5 - Graph -3 ≤ x**

*What is different about this example?*

Students should notice that the number is first and the variable is second.

*How would we interpret this inequality? *

Students should suggest either "-3 is less than or equal to x" or "x is greater than or equal to -3".

*What value of x makes this true?*

Students should give answers of -3 or greater. This will help them when determine which direction to shade the number line.

10 minutes

The Independent Practice will assess students' understanding of the lesson. Students will have to create a number line and graph each inequality. To ensure that students understand the inequality and its' solutions, they will have to give a possible value that would be part of the solution set.

Students may have difficulty with 3 - 5 because these needed to be translated first. I will suggest to students that they use their Writing Algebraic Inequalities Chart to help them interpret and translate the key words.

**Independent Practice**

Graph the solution to each inequality. Write one value that could be a possible solution.

1) x < -1

2) 0 < y

3) Carl has at least $5.

4) Tyrone has more than $3.

5) Vanessa has at most $8.

After 10 minutes, we will discuss students' work and answers.

5 minutes

It is important that students are able to interpret inequalities that have already been graphed. For the Graphing Inequalities Lesson Summary, students will answer the following questions:

*Is there a minimum value for the inequality?*

*Is there a maximum value for the inequality?*

*What is a possible solution for the inequality?*

*What is the inequality?*