1. Essential Question: How do you solve and graph one step inequality?
Lesson Solve Inequalities Using Addition, Subtraction, Multiplication and Division
Essential Question: How do you solve and graph one step inequality?

2. Before we start…
You know that you can send no more than 50 text messages on your monthly cell phone plan without incurring additional charges. You sent 18 messages yesterday and 9 today. How many messages can you send the rest of the month without additional charges?

3. What is the graph of an inequality?
It consists of all points on a number line that represent solutions.

4. How do you graph an inequality?
You will make a circle on the number given.
If it’s equal to you will fill it in
If it’s not equal to you will leave it open
Then draw an arrow from the circle in the direction of the inequality
To the right if it’s greater than
To the left if it’s less than

5. Graph

6. Graph

8. What is a linear inequality?
A statement comparing two real numbers. It can be written in the following forms:

9. What is a solution of an inequality?
A value that, when substituted for the variable, results in a true statement.

10. How do you solve a linear inequality?
You isolate the variable using inverse operations.
Inequalities are solved similarly to equations.
However, when multiplying and dividing by negatives you must REVERSE the inequality symbol.
Graph your solution on a number line.

11. What are equivalent inequalities?
Inequalities that have the same solutions as the original inequality.

12. Transformations That Produce Equivalent Inequalities
Transformation Applied
Original Inequality
Equivalent Inequality
Add the same number to each side.
Subtract the same number from each side.
Multiply each side by the same positive number.
Divide each side by the same positive number.
Multiply each side by the same negative number and reverse the inequality.
Divide each side by the same negative number and reverse the inequality.

21. Luggage Weights You are checking a bag at an airport
Luggage Weights You are checking a bag at an airport. Bags can weigh no more than 50 pounds. Your bag weighs 16.8 pounds. Find the possible weights w (in pounds) that you can add to the bag.

22. Internet You earn points from buying items at an Internet shopping site. You would like to redeem 2350 points to get an item for free, but you want to be sure to have no more than 6000 points left over. What are the possible number of points you can have before making a redemption?

23. Music You have $30 to buy songs for your friend’s party
Music You have $30 to buy songs for your friend’s party. The songs cost $1.29 each on iTunes. What are the possible numbers of songs that you can buy?

24. How do you solve and graph an inequality?

25. Ticket Out the Door