1. Compound Inequalities

2. What is a compound inequality? A compound inequality joins two inequalities with either “and” or “or”.

3. “AND” vs. “OR” “AND” Inequalities ‘And’ means intersection—what do these two inequalities have in common? Where do they over lap? For example: an iPhone must be used in temperatures that are greater than 32° AND less than 95° What are some temperatures that you can use an iPhone in? “OR” Inequalities ‘Or’ means union– if you are in one set, you are in the solution For example: in order to qualify for discounted tickets at most ski mountains, you must be under 12 years old OR over 65. What are some ages of people who would get a discounted ticket?

4. Graphing ‘And’ Inequalities

5. Graphing ‘Or’ Inequalities

6. Writing ‘Or’ Inequalities from a graph To write an ‘or’ inequality from a graph, simply write both inequalities shown, and write ‘or’ between them! Example: Write the inequality shown below

7. Writing ‘And’ Inequalities from Graphs ‘And’ inequalities represent numbers between two different values, and can be written as a single inequality. We can start with two inequalities What numbers does this represent? We can write the first inequality so that the number comes first. When written like this, it’s easy to see that this represents all the numbers between 3 and 7, with 7 included.

8. Writing ‘And’ Inequalities from Graphs To write ‘and’ inequalities from a graph: Write the two numbers that are the end points of the graph Write an x in the middle Add in two less than signs between the numbers and the x Add an ‘or equal to’ line where necessary

9. Write the inequality below. In order to ride the tilt-a whirl at the fair, you must weight more than 90 pounds. The weight limit is 250 pounds. Write as an inequality. Your doctor’s office is open between 8:00 am and 4:00 pm. Make a graph to show when you would NOT be able to go to the doctor’s. Ex. 1 Ex. 2 Ex. 3 Ex. 4 Intro to Compound Inequalities 15 10/2 1 16 10/2 1

10. Solving Compound Inequalities Practice

17. A box of cereal must weigh more than 629.4 grams and less than 630.6 grams to pass inspection. The box itself weighs 5.5 grams. What are the possible weights for the cereal?