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|x| is "absolute value" -- the distance of the number to 0.
(x) is just a grouping.
|-6| = 6
(-6) = -6
The next question is what is the value of -(-6).
(-6) equates to -6. So the negative value of that result is 6.
What is the value of -(-(-6)?
This is an error. The parenthesis don't match. There are two on the left and one on the right.
If it is actually written -(-(-6)) then, breaking it down by groupings,
(-6) = -6
-(-6) = 6
-(-(-6)) = -6
It helps to think of subtracting when using -. Since no number is subtracted, you are subtracting zero.
So (0 - 6) = -6
0 - (0 - 6) = 6
0 - (0 - (0 - 6) ) = -6
Try it on a calculator. Just do the innermost () equation first, save the result, and apply that result to the next operation.
On the calculator,
Innermost parens: 0 - 6 = -6
Middle parens: 0 - -6 = 6
0 - (middle parens, result above) 6 = -6
_______________________________________
Clarence Donath
Richmond, RI
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