1. Compound Inequalities A compound inequality is either two inequalities separated by a word, or an expression in between two inequality symbols.

2. Compound Inequalities A compound inequality is either two inequalities separated by a word, or an expression in between two inequality symbols. Let’s look at the first type…separated by a word

3. Compound Inequalities There are two words that can appear in between inequalities AND / OR

4. Compound Inequalities There are two words that can appear in between inequalities AND / OR With AND, the solution set is what is shared or common

5. Compound Inequalities There are two words that can appear in between inequalities AND / OR With AND, the solution set is what is shared or common With OR, the solution set is all solutions combined

6. Compound Inequalities There are two words that can appear in between inequalities AND / OR With AND, the solution set is what is shared or common With OR, the solution set is all solutions combined We are going to use a line graph to help us find the solution set…

7. Compound Inequalities

11. STEP # 2 : Set up a number line and graph your points

12. Compound Inequalities -10

13. Compound Inequalities -10

14. Compound Inequalities STEP # 2 : Set up a number line and graph your points -10 STEP # 3 : With AND in between the expressions, we need to find where the graphs are ON TOP of each other

15. Compound Inequalities STEP # 2 : Set up a number line and graph your points -10 STEP # 3 : With AND in between the expressions, we need to find where the graphs are ON TOP of each other THIS IS OUR SHARED AREA

16. Compound Inequalities STEP # 2 : Set up a number line and graph your points -10 STEP # 3 : With AND in between the expressions, we need to find where the graphs are ON TOP of each other Mesh the ”shared area “ into one line

17. Compound Inequalities

18. STEP #1 : Solve each inequality Remember, when you divide by a negative, the inequality changes direction

19. Compound Inequalities STEP #1 : Solve each inequality STEP #2 : Set up a number line, graph your points and draw your arrows

20. Compound Inequalities STEP #1 : Solve each inequality STEP #2 : Set up a number line, graph your points and draw your arrows closed circle and to the right open circle and to the right

21. Compound Inequalities STEP #1 : Solve each inequality STEP #2 : Set up a number line, graph your points and draw your arrows closed circle and to the right open circle and to the right STEP # 3 : With OR in between the expressions, we will look at all possible solutions. Since the arrow for (+3) joins and is in the same direction as (+5), the solution set is all numbers greater than (+3) FINAL graph

22. Compound Inequalities The other type of compound inequality that occurs is when there is an expression squeezed in between two inequalities.

23. Compound Inequalities

24. If I covered the left side of the equation and only solved for the right side, I would add 8 to both sides… +8 = +8

25. Compound Inequalities When solving these types, whatever you would do to solve one side, you would also do to solve the other side… +8 = +8 = +8

26. Compound Inequalities +8 = +8 = +8

27. Compound Inequalities +8 = +8 = +8

28. Compound Inequalities +8 = +8 = +8 Set up your number line and graph the points… Open circles

29. Compound Inequalities +8 = +8 = +8 Open circles If both inequality symbols point to the LEFT, the solution is SQUEEZED in between your points…

30. Compound Inequalities +8 = +8 = +8 Open circles If both inequality symbols point to the LEFT, the solution is SQUEEZED in between your points… If both inequality symbols point to the RIGHT, the solution HAS A GAP in between your points…