High School Math : Understanding Absolute Value
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Example Questions
Example Question #1 : Absolute Value
Expression 1:
Expression 2:
Find the set of values for 
All values where
All values where
All real numbers
All values where
All values where
All values where
In finding the values for 
The first possibility is described by the inequality:
If you think of a number line, it is evident that there is no solution to this inequality since there will never be a case where subtracting from 
The second possibility, wherein 
We can simplify this inequality to find that 
The third possibility can be represented by the following inequality (where the sign is inverted due to multiplication by a negative):
This is again simplified to 
The final possibility is represented by the inequality
This inequality simplifies to 
The only possible condition that satisfies the inequality is that which arises in two of the tested cases, when 
Example Question #2 : Absolute Value
What is the absolute value of -3?
10
1
3
9
-3
3
The absolute value is the distance from a given number to 0. In our example, we are given -3. This number is 3 units away from 0, and thus the absolute value of -3 is 3.
If a number is negative, its absolute value will be the positive number with the same magnitude. If a number is positive, it will be its own absolute value.
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