6.5 Absolute Value Equations and Inequalities pg. 300 to 306

Absolute Value Equations:2 answers ( a + one and a - one)

Absolute Error is absolute value of the difference betweent he actual measure and the specified measure

Absolute Value Equations allow you to FIND the greatest and least acceptable values

Because it is ABS there will be 2 answers!!!!!!

So what do you do.......You solve the equation in 2 cases...

Meaning-- you solve the equation 2 times and get 2 answers

d - 3.50 = 0.01

d - 3.50 = + 0.01 d - 3.50 = - 0.01

d - 3.50 = 0.01 d - 3.50 = 0.01

CASE 1Pretend "answer" is +

AND drop off ABS signs

CASE 2Pretend "answer" is -

AND drop off ABS signs

+ 3.50 +3.50

d = 3.51

+ 3.50 +3.50

d = 3.49

ANSWERS!!!!Will always have 2 with ABS value

Try more.....

Solve 2x - 4 = 8 Solve 2x + 21 = 33

WHAT happens if you start with 5x - 2 = -12 ?

Absolute Value Inequalities...

-- 2 cases again-- 2 answers--ONLY difference is that you have inequality signs and can graph

them!

CASE 1Pretend "answer" is +

Solve and graph

CASE 2Pretend "answer' is -

Solve and graph

x - 48 ≤ 15

x - 48 ≤ + 15 x - 48 ≥ - 15

x - 48 ≤ 15

x - 48 ≤ 15

+ 48 + 48

x ≤ 63

+48 + 48

x ≥ 33

6333

What did you notice here?

Lets try more....

x - (-5) ≤ 2

x - (-5) ≤ 2

x - (-5) ≤ 2

x - (-5) ≤ 2

x - (-5) ≥ - 2

x + 5 ≤ 2-5 -5

x ≤ -3

x + 5 ≥ -2 -5 -5

x ≥ -7

1. Drop off ABS signs

2. Case 2 change "answer" to -AND flip sign

3. Combine like terms

4. Combine inequalities if you can

5. Graph

-7 ≤ x ≤ −3

-7 -3

Try again....

x + 6 ≤ 4

How can you tell that x - 5 ≤ -1 is no solution?

Try some more..... pg. 305 # 5-15 in groups.Keep it down!!!!