CF4i - Solving Absolute-Value Equations
Recall that absolute value of a number is that number's
distance from zero on the number line.
Use the above definition to solve the following:
x = -
case 1
|x|=7
Type in your answer(s).
case 2
x= +
The first step to solving an absolute value equation is to
determine if the absolute value expression is isolated.
    Why? Because there is nothing
on the outside of the absolute bars -
                before or after.
|-5x-1|
|2x+4|
Isolated
|x+5|
|7x|
|x|
Click "OK" to go to the next slide.
Why? Because of what's
    highlighted in red.
5
NOT Isolated
 |x+8|
|x-3|
4
 |x+2|
|3x|
2
 |x|
+12
-6
+2
Add         to both sides
      The absolute value
 expression is now isolated
|4x|-9=11
|x|+6=12
Use the inverse operation(s) if an absolute
       value equation is NOT isolated.
-6  -6
|x|=6
   What will it take to isolate
the absolute value expression?
Type in your answer(s).
Divide both sides by 
      The absolute value
 expression is now isolated
2|x|=16
2        2
5|x|=25
|x|= 8
Click "OK" to go to the next slide.
x+4=-9
case 1
-4  -4
x=-13
  Step 2: Once the absolute value expression                    has been isolated,the definition of absolute value can be applied.
|x+4|=9
    Split the equation into 2 cases                        andsolve for x using inverse operations
x+4=+9
case 2
-4   -4
x=+5
 Isolated? YES!
2x-4=-12
case 1
+4   +4
2x=-8
2      2
x=-4
|2x-4|=12
2x-4=+12
case 2
+4   +4
2x=+16
2        2
x=+8
Dropped the bars and made one
equal to -9 and the other to +9
x+4=-9
case 1
-4  -4
x=-13
Solutions to the equation
Used inverse operation
|x+4|=9
Type in your answers from SMALLEST to LARGEST.
Did you see how the definition of
 the absolute value was applied?
x+4=+9
case 2
-4   -4
x=+5
 Isolated? YES!
   Now SPLIT!
2x-5=
x=
case 1
Now complete the problem by
   using inverse operations
Now you try one!
|2x-5|=15
2x-5=
x=
case 2
Solve the following  equation:
Now that we have broken down all the steps to solving
an absolute value equation, let's solve one from scratch.
4x=
x=
|4x|- 6  =  34
case 1
|4x| =
4x=
case 2
x=
Step 1: Isolate the absolute
value expression by using
inverse operations
Step 2: Split into 2 cases
Step 3: Solve using
inverse operation(s)
Type in your answer(s)
x=
Try this one totally on your own:
|x+2| - 5 = 8
Type in your answer from SMALLEST to LARGEST.
Remember: Isolate, Split, Solve
x=
x=
Try this one totally on your own:
Type in your answer from SMALLEST to LARGEST.
Remember: Isolate, Split, Solve
3|x+2| = 18
x=
|x|=
There is a special case. It occurs                             .
If the absolute value expression
            , there will be                       .
number
-7
Here are some example:
|3x+6|=
Click "OK" to go to the next slide.
|x-3|=
All of these equations
  have NO SOLUTION
NO SOLUTION
-5
-4
is equal to a negative
after the isolation
|7x|=
-2
Solve the following equation:
|3x + 5| + 9 = 3
How many solutions did you find?
Try this one on your own.
No solution
1-solution
2-solutions
Choose the best answer.
Remember to isolate first!
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