Math Skill: Absolute Value 2
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Absolute Value 2

This topic continues the topic of absolute value.
To review the basics of absolute value, see here.

You may also find a review of Integer Addition and Integer Subtraction to be useful.

Remember that the absolute value of any number is always positive.

When absolute values appear in equations, simplify the absolute values to make it easier to solve.
 3 + | 4 | = 3 + 4 3 - | 4 | = 3 - 4 3 + | -4 | = 3 + 4 3 - | -4 | = 3 - 4

Examples:

Evaluate.
 a. | 0 | + | -5 | - | 8 | = 0 + 5 - 8 = b. | -4 | + | -2 - -1 | = 4 + | -2 + 1 | = 4 + | -1 | = 4 + 1 = Start from the inner absolute values and work your way out. c. || 2 + 7 | - | -5 + -5 || = || 9 | - | -10 || = | 9 - 10 | = | -1 | =

### Complexity=5, Mode=2

Evaluate.
 1.   |- 1| + |2| 2.   |2| - |- 1|

### Complexity=5, Mode=3

Evaluate.
 1.   |- 1| + |- 1| + |3| 2.   ||- 3 - 1| - |1||

### Complexity=8, Mode=4

Evaluate.
 1.   |- 4 + - 1| + |1 + 7| 2.   |8 + 2| + |4| + |- 7|

### Complexity=9, Mode=6

Evaluate.
 1.   ||5| - |9 + 3| - |- 6 + 8| - |- 5|| 2.   |6 - - 1| - |- 3| - |- 3| - |- 3 - 7|

### Complexity=10, Mode=8

Evaluate.
 1.   |- 3| - |3 - 9| - |- 2 - 2| - |- 1| - |0| - |- 1| 2.   |10 + 0| - |- 7| - |- 8 - 5| - |- 7| - |4 + - 8|

Evaluate.
1|- 1| + |2|
Solution
|-1| = 1

1 + 2 = 3
2|2| - |- 1|
Solution
|-1| = 1

2 - 1 = 1

### Complexity=5, Mode=3

Evaluate.
1|- 1| + |- 1| + |3|
Solution
|-1| = 1

|-1| = 1

1 + 1 + 3 = 5
2||- 3 - 1| - |1||
Solution
- 3 - 1 = - 4
|-4| = 4

4 - 1 = 3

### Complexity=8, Mode=4

Evaluate.
1|- 4 + - 1| + |1 + 7|
Solution
- 4 + - 1 = - 5
|-5| = 5

1 + 7 = 8
5 + 8 = 13
2|8 + 2| + |4| + |- 7|
Solution
8 + 2 = 10
|-7| = 7

10 + 4 + 7 = 21

### Complexity=9, Mode=6

Evaluate.
1||5| - |9 + 3| - |- 6 + 8| - |- 5||
Solution
9 + 3 = 12
- 6 + 8 = 2
|-5| = 5

5 - 12 - 2 - 5 = - 14
|-14| = 14

2|6 - - 1| - |- 3| - |- 3| - |- 3 - 7|
Solution
6 - - 1 = 7
|-3| = 3

|-3| = 3

- 3 - 7 = - 10
|-10| = 10

7 - 3 - 3 - 10 = - 9

### Complexity=10, Mode=8

Evaluate.
1|- 3| - |3 - 9| - |- 2 - 2| - |- 1| - |0| - |- 1|
Solution
|-3| = 3

3 - 9 = - 6
|-6| = 6

- 2 - 2 = - 4
|-4| = 4

|-1| = 1

|-1| = 1

3 - 6 - 4 - 1 - 1 = - 9