Absolute Value Equations
Remember:  
Don't take this before the 3.6a lesson!
Absolute Value    Equations
You will get TWO answers!
So, 
Simplify.  
x   = 4 means that 
4    = 4
-4  = 4
x = 4 or x = 
a) Write two equations
b) Isolate the absolute value expression
c) Solve each equation
d) Make sure the number on the right     is positive or zero
e) Write the two answers
Put the steps in order.
a, b, c, d, e
b, d, a, c, e
d, b, a, c, e
b, a, d, c, e
In which step is the first mistake?
3.
1.  3x + 5 = 4 or 3x + 5 = -4
2.  
Step 1
Step 2
3x = 9
x = 3
3x + 5  = 4
Step 3
Step 4
4.         3x = -9
5.
x = -3
Which operation needs to be done to
isolate the absolute value expression for
3
c - 2  = 9
subtract 2
multiply by 3
divide by 3
distribute the 3
?
Which operation needs to be done
to isolate the absolute value expression?
4x + 1
subtract 5
divide by 4
subtract 1
add 5 
- 5 = 14
?
4
Which operation should be done first?
3y - 2   + 1 = 9
distribute the 4
subtract 1
divide by 4
add 2
?
Whew!  That was close.  Now, try solving!
z + 1  = 3
z = 2
z = 2, -2
z = 2, -4
no solution
Solve
m - 5   = 9
m = 14
m = 14, -14
m = -4, 14 
no solution
Solve
4p - 8   = 12
p = 1, 5
p = -5, 1
p = 5, -1
no solution
Solve
-2k - 4   = 16
k = - 10, 6
k = 10, -6
k = 6, -6
no solution
Solve
2x + 1  = -11
x = -5, 6
x = -6, 5
x = 5, 6
no solution
Are you ready for a few more?
Solve
5v - 4  = 21
Sure you are!
v = 5
v = 5, -17/5
v = 5, -5
no solution
Solve
2
+ 1  = 4
x = 6, 10
x = -6, -10
x = 6, -10
no solution
Solve
2
w - 3 
= 8
w = 0, 6
w = 7, -1
w = 7
no solution
Solve
-3
t = -1 or 2
t = -1 or -6
t = -1 or -7
no solution
t + 4
= -9
Okay, if you missed that last one, do not go on
without looking at your notes!
Solve
-4
2x
no solution
x = 2 or -2
x = -2, 1/2
x = -2
= 16
Solve
3b
b = 4, -8
b = -4, -8
no solution
b = 4, -4
+ 6 
= 18
Solve
3
-2d + 6
d = 1, -9
no solution
d = 1, 5
d = 1
= 12
What does this mean?  The answer should have been what?  
Robby was solving the equation belowand got 4 and (-10) as his answers.
If you substitute -10 for d, what does the left hand side equal?
If you substitute 4 for d, what does the left hand side equal?
Fill in all the blanks before clicking "ok".
-4  3d - 6
= 24
(no capitals)
Are 4 and (-4) the solutions to
4x = 16
Yes
No
?
Are -2 and 1 solutions to
2  4y + 2 
Yes
No
= 12
?
Are -1 and 5 solutions to
-3  q - 2
Yes
No
= 9
?
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