Simplifying and Solving
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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
Absolute Value– The absolute value of a number is the
distance from zero

Since distance can not be negative, the absolute value of a
number is always positive.

However, that does not mean that an absolute value
equation will only have positives value for the variable.

Absolute value equation have two solutions because you
can move in two different directions on the number line.
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What is the absolute value of
3
?
Ask yourself, how many
steps do you take to 3?
3
Absolute value is 3
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What is the absolute value of
8
?
Ask yourself, how many
steps do you take to -8?
8
Absolute value is 8
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9
_
What is the absolute value of
?
Ask yourself, how many
steps do you take to 9?
9
But have we used the negative sign yet?
9
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What is the absolute value of 
7
?
_
Ask yourself, how many
steps do you take to -7?
7
But have we used the negative sign yet?
7
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 Step
1– simplify the expression
inside the absolute value sign
 Step
2– Take the absolute value
 Step
3– Simplify the expression
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87
15
15
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1 7
1  7 
6
6
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 46
_
10
10
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_
 83
_
5
5
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_


1.
2.
3.
4.
Absolute Value– The absolute value of a number is
the distance from zero
Absolute value equation have two solutions
because you can move in two different directions
on the number line.
Isolate the absolute value sign
Separate the equation into the two possible
equations
Solve for the variable
Check solutions
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The absolute value of x is the distance from zero.
If | x | = 4
Start
Here
-6
-5 -4
-3 -2
-1
0
1
2
3
4
5
6
Therefore x = 4 or -4 because they are both 4 steps away
from zero.
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The absolute value of x is the distance from zero.
If | x | = -5
Start
Here
Think about it
-6
Wait!!!!
-5 -4
-3 -2
-1
0
1
2
3
4
5
6
Can we take -5 steps?
No, distance is always positive
therefore its No Solution
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1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
3. Solve for the variable
4. Check solutions
x3  5
8  3  5
23  5
5  5
5 5
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1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
3. Solve for the variable
4. Check solutions
x4 7 8
x  4 1
3 4  7  8
1  7  8
1 7  8
54 7  8
1 7 8
1 7  8
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1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
2 x6 8
4. Check solutions
2
2
x6  4
x  6  4
x6 4
6  6
6  6
x   10
x 2
3. Solve for the variable
2 10  6  8
2 4  8
2  4  8
2 2  6  8
2 4 8
2  4  8
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1.
2.
3.
4.
Isolate the absolute value sign
Separate the equation into the two possible equations
Solve for the variable
2 x  6  8  2
Check solutions
8  8
2 x6  6
2
2
x6  3
x  6  3
x6  3
6  6
6  6
x 9
x 3
2 3  6  8  2
2 3  8  2
2  3  8  2
6  8  2
2 9  6  8  2
2 3  8  2
2  3  8  2
6  8  2
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1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
2 3x  5  8
2
2
3x  5  4
3 x  5  4
Wait !!!!
Think about it…
Can we take -4 steps?
No, distance is
always positive
x  No solution
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