How do you simplify #-|8 -2| - |1 - 6| +|3 -4| - |2 +5| #?

1 Answer
KillerBunny
Oct 1, 2016

#-17#

Explanation:

Just remember how the absolute value works: it always returns the positive version of the number it has inside itself. So, the absolute value of a positive number is the positive number itself, while the absolute value of a negative number is the positive version of that number. In formulas:

#|24| = 24#, and #|-57| = 57#

So, let's see what's inside your absolute values: your equation is

#-|8-2|-|1-6|+|3-4|-|2+5|#

Doing the sums and differences inside the absolute values gives

#-|6|-|-5|+|-1|-|7|#

And now use what I said at the beginning: the absolute value of #6# is #6#, the absolute value of #-5# is #5#, the absolute value of #-1# is #1#, and the absolute value of #7# is #7#, and thus we have

#-6-5+1-7=-17#

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