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Absolute Value Equations
Contributed by: Miles
(Original author: Jarvie)
Remember:  
Absolute Value    Equations
Absolute value equations might have 
one answer, two answers or no answer.
So, 
Simplify.  
x   = 4 means that 
4    = 4
-4  = 4
x = 4 or x = 
Which operation needs to be done to isolate 
the absolute value expression for this equation?
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
Solve the equation.
z + 1  = 3
z = 
z + 1  = 3
or
or
z + 1  = 
z = 
Solve the equation.
m - 5   = 9
m = 14
m = 14, -14
m = -4, 14 
no solution
Solve the equation.
4p - 8   = -12
p = 1, 5
p = -5, 1
p = 5, -1
no solution
Solve the equation.
-2k - 4   = 16
k = - 10, 6
k = 10, -6
k = 6, -6
no solution
Solve the equation.
2x + 1  = -11
x = -5, 6
x = -6, 5
x = 5, 6
no solution
Solve the equation.
2
+ 1  = 4
x = 6, 10
x = -6, -10
x = 6, -10
no solution
Solve the equation.
2
w - 3 
= 8
w = 0, 6
w = 7, -1
w = 7
no solution
Solve the equation.
-3
t = -1 or 2
t = -1 or -6
t = -1 or -7
no solution
t + 4
= -9
Solve the equation.
-4
2x
no solution
x = 2 or -2
x = -2, 1/2
x = -2
= 16
Solve the equation.
3
-2d + 6
d = 1, -9
no solution
d = 1, 5
d = 1
= 12
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