1. Unit 2: inequalities
Final Exam Review

2. Topics to cover Graphing Inequalities Solving Inequalities
Word Problems
Compound Inequalities

3. Graphing Inequalities
In this unit, we learned how to graph inequalities on NUMBER LINES
There are 2 things you must take care of:
What type of circle to use (OPEN OR CLOSED)
Which way to draw the arrow (LEFT OR RIGHT)
Circle:
Open: > OR <
Closed: ≥ OR ≤
Arrow:
Left: < OR ≤
Right: > OR ≥

4. Graphing Inequalities
Example: x < 2
g ≥ -4
You Try!
1. m ≤ w > > d (be careful)

5. Graphing Inequalities
Going Backwards!
Example: s ≤ -2
h > -2
You Try! 3.

6. Solving inequalities
You solve inequalities very similar to solving EQUATIONS
First, COMBINE LIKE TERMS, then solve for the variable.
To finish the problem, GRAPH the inequality.
BE CAREFUL! Whenever to multiply or divide by a NEGATIVE NUMBER, you must SWITCH the inequality
Example: x + 5 ≥ 3
Subtract 5  x ≥ -2
Divide by -2 (SWITCH THE SIGN)  x ≤ 1

7. Solving inequalities You Try! 1. 3(x + 1) < 15 2. 4x + 18 ≥ 2
3. -4x – 5 < x – (-2) > 5x – 12

8. Word Problems Inequality word problems use a lot of vocabulary.
Here is a list of the words that go with each symbol:
> 
More Than
Above
Greater Than
< 
Less Than
Below
Fewer Than ≥
At Least
Minimum
No Less Than ≤
At Most
Maximum
No More Than

9. Word Problems
Example: The sum of five times a number and two times and number is at least fourteen.
5x + 2x ≥ 14
7x ≥ 14
x ≥ 2

10. Word Problems
You Try!
The product of a number and three is less than negative twelve
Five less than a number is under eleven
Negative six times a number is at most forty-eight

11. Compound inequalities
Compound Inequalities occur when you have 2 different inequalities written TOGETHER and graphed on the SAME number line.
Example: 𝒙<𝟐 𝒐𝒓 𝒙>𝟒
𝒙≥𝟏 𝒂𝒏𝒅 𝒙≤𝟔

12. Compound inequalities
You Try!
Graph the following compound inequalities
1. 𝒙<𝟒 𝑶𝑹 𝒙≥𝟖 2. 𝒙>𝟐 𝑨𝑵𝑫 𝒙<𝟔

13. Compound inequalities
Solving Compound Inequalities
SEPARATE the inequality into 2 different inequalities.
REPEAT the term in the middle
Example: -1 < x + 9 < 17
Separate  < x and x + 9 < 17
Solve  < x and x < 8

14. Compound inequalities
You Try!
𝟏𝟐<𝟐𝒙+𝟐≤𝟐𝟎
𝟑𝒙−𝟏≤𝟓<𝟒𝒙+𝟏𝟑

15. ALL DONE