1. Mr. Peter Richard’s Awesome Algebra Students Will Be Solving COMPOUND Inequalities

2. Greater than or equal to
Inequality Symbols
Less than
Not equal to
Less than or equal to
Greater than or equal to
Greater than

3. Transformations for Inequalities
Add/subtract the same number on each side of an inequality
Multiply/divide by the same positive number on each side of an inequality
If you multiply or divide by a negative number, you MUST flip the inequality sign!

4. Graphing Linear Inequalities
Remember:
< and > signs will have an open dot o
and signs will have a closed dot
graph of graph of 4 5 6 7 -3 -2 -1

5. Compound Inequality An inequality joined by “and” or “or”. Examples
think between
think oars on a boat

6. Solve & graph. -9 -9 +8 +8 -6x < -6 -3x > 21
-6x+9 < 3 or -3x-8 > 13
-6x < x > 21
x > or x < -7
Flip signs
Think oars -7 1

7. Example: Solve & graph. -9 < t+4 < 10 -4 -4 -4 -13 < t < 6
Think between!
-13 6

8. Reverse Both Inequalities
Example: Solve –x + 3 < -2 or
-4 – x > 5, then graph.
–x + 3 < -2 or -4 – x > 5
-x < -5 or x > 9
x > 5 or x < -9

9. 4) Graph the compound inequality 6 < m < 8
When written this way, it is the same thing as
6 < m AND m < 8
It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however,
it is easier to graph everything
between 6 and 8! 7 8 6 o

10. 3) Which inequalities describe the following graph?-2 -1 -3 o
y > -3 or y < -1
y > -3 and y < -1
y ≤ -3 or y ≥ -1
y ≥ -3 and y ≤ -1

11. Solve This Yourself! Example: Solve -9 ≤ -4x – 5 < 3. Graph.
-4 ≤ -4x < 8
1 ≥ x > -2

12. Try This 1, 2! Example: Solve -4 ≤ x – 3 < 6. Then graph.
- 1 ≤ x < 9

13. Show What you Know! Quiz: Page 230 # 6, 8, 24, 28, 32
Homework: # 5, 9, 13, 21, 27