Definition of absolute value
Definition of absolute value: the absolute value of a number is the distance the number is from zero
Look at the following two graphs:
The first one shows 6 located at a distance of 6 units from zero.
We write 6 = 6
The second one shows 8 located at a distance of 8 units from zero.
We write 8 = 8
You can see from this that the absolute value of a number is always positive with the exception of taking the absolute value of 0 (0 = 0)
Therefore, do not write 5 = 5 or 4 = 4 please!
6 means distance from 0 to 6
8 means distance from 0 to 8
For 8 = 8, you could also argue that to get 8, you have to take the negative of 8 since   8 = 8
So,   8 =   8 = 8
This observation helps us to come up with a formal definition of absolute value
 x  = x if x is positive or zero, but x if x is negative
This definition is important to understand before solving absolute value equations or absolute value inequalities
Calculate the absolute value of the following numerical expressions
1) 4
^{2} − 4 × 2
2) 5 + 5 × 2 − 15
3) 8 + 2 × 5
1)
 8 + 2 × 5  =  8 + 10 
 8 + 2 × 5  =  2 
 8 + 2 × 5  = 2
2)
 4
^{2} − 4 × 2 =  16 − 4 × 2
 4
^{2} − 4 × 2 =  16 − 8
 4
^{2} − 4 × 2 =  8 
 4
^{2} − 4 × 2 = 8
3)
5 + 5 × 2 − 15 =  5 + 10 − 15 
(5 + 5 × 2 − 15) =  5 − 15 
(5 + 5 × 2 − 15) =  15 
(5 + 5 × 2 − 15) = 15

Oct 15, 18 11:05 AM
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