1. Algebra 2 09/19-20/16 EQ: How do I solve absolute value equations and inequalities? How do I solve compound inequalities HW: pg 154 # 3-35 all (due wed) Bring textbook - sub Quiz corrections

2. Solve compound inequality
2 types of problems
AND < 3x -5 < 10
AND < 3x AND x + 8 < 18
OR < 3x R x > 18

3. 2 ≤ 3x – 4 < 11
2 ≤ 3x – 4 6 ≤ 3x 2 ≤ x 3x – 4 < 11 3x < 15 x < 5

4. 1 2 c ≥ -2 AND 2c + 1 < 1
Solve and Graph

5. x – 5 < OR -2x≤ -10
Solve and Graph

6. AND or OR
What are the differences and similarities between solving and graphing AND Or inequalities?
Similarities:
Differences:

7. Absolute Value | |
Absolute value measures the distance from zero. Absolute value is always positive | 5 | = 5 |-5| = 5

8. Solving equations |3x + 14| = 7
Break into 2 parts Positive 3x + 14 = x = -7 x = −7 3 Negative 3x + 14 = x = - 21 x = -7

9. |x + 3| - 9 = 5
Simplify outside first by adding 9 to both sides, than separate into 2 parts | x + 3| =14 x + 3 = 14 x + 3 = -14 x = 11 x = -17
POSITIVE SIDE
NEGATIVE SIDE

10. 2|x + 5| = 14
Our goal is to get the absolute value by itself so divide both sides by 2. NEVER DISTRIBUTE A NUMBER INSIDE THE ABSOLUTE VALUE!!!!! | x + 5 | = 7 x + 5 = 7 x + 5 = -7 x = 2 x = -12
POSITIVE SIDE
NEGATIVE SIDE

11. |3x – 4| + 6 = 3
Isolate | | (absolute value by subtracting 6) |3x -4| = -3 Recall the definition of absolute value (distance from zero and makes the answer positive). Can we have a negative answer (-3)? No In this case we have NO SOLUTION!

12. -3|x +5| + 7 = -2 -3|x + 5| + 7 = -2 subtract 7 to both sides
-3|x + 5| = divide both sides by -3
|x + 5| = break into 2 problems
x + 5 = x + 5 = -3
x = x = -8

13. Know it. Copy the table of pg151 in your notes
Know it!!! Copy the table of pg151 in your notes. Critical Thinking What connections can you make to graphing inequalities? ( Hint: AND / OR graphs)

14. |2x – 1| > 5 What kind of graph?
Is greater than… mORe answers OR graph
Split into 2 parts (note what happens on the negative side)
2x -1 > x -1 < -5
2x > x < -4
x > x < -2

15. |3x + 1| ≤ 8 What kind of graph? Is less than… less answers AND graph
Split into 2 parts (note what happens on the negative side)
3x -1 ≤ x -1 ≥ -8
3x ≤ x ≥ -7
x ≤ x ≥ about -2.33

16. -4|x + 3| +8 > 4 -4|x + 3| > - 4 subtracted 8 from both sides
|x + 3| < divided by -4 (flipped inequality)
separate into 2 parts
x + 3 < x + 3 > -1
x < x > -4

17. -4|x + 3| +8 < 12 -4|x + 3| < 4 subtracted 8 from both sides
|x + 3| > divided by -4 (flipped inequality)
Even though we got a negative number, we can come up with numbers that are bigger than -1 (0, 1, 2, …)
x + 3 > OR x + 3 < 1
x > OR x < -2
ALL REAL NUMBERS

18. -4|x + 3| +8 > 12 -4|x + 3| > 4 subtracted 8 from both sides
|x + 3| < divided by -4 (flipped inequality)
Can the absolute value produce a value that is less than a negative number?
No - therefore, there is no solution