6.5 Absolute Value Equations and Inequalities pg. 300 to 306
Absolute Value Equations:
2 answers
Absolute Error is absolute value of the difference between the
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
CASE 1
Pretend "answer" is +
AND drop off ABS signs
CASE 2
Pretend "answer" is AND drop off ABS signs
d - 3.50 = 0.01
d - 3.50 = 0.01
d - 3.50 = + 0.01
+ 3.50
+3.50
d - 3.50 = - 0.01
+ 3.50
+3.50
d = 3.51
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!
x - 48 ≤ 15
CASE 1
Pretend "answer" is +
Solve and graph
CASE 2
Pretend "answer' is Solve and graph
x - 48 ≤ 15
x - 48 ≤ 15
x - 48 ≤ + 15
+ 48 + 48
x - 48 ≥ - 15
+48 + 48
x ≤ 63
x ≥ 33
What did you notice here?
33
63
Lets try more....
x - (-5) ≤ 2
1. Drop off ABS signs
2. Case 2 change "answer" to AND flip sign
3. Combine like terms
4. Combine inequalities if you can
-7
-3
5. Graph
Try again....
x+6 ≤ 4
How can you tell that x - 5 ≤ -1 is no solution?
To sum up:
1. ABS value EQUATIONS
Split into 2 cases--one + and one SOLVE BOTH and you have 2 answers
2. ABS Value INEQUALITES
Split into 2 cases--ONE EXACTLT how the probelm is
ONE where you- CHANGE number on right to
NEGATIVE AND you FLIP the inequality
SOLVE each one-- graph on number line
3. "TRICKS" ABS can NEVER come out negative sooo....
IF YOU SEE........THEN THERE is NO SOLUTION
Try some more..... pg. 305 # 5-15 in groups.
Keep it down!!!!