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

1 Answer
KillerBunny
Oct 1, 2016

-17−17

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|24|=24, and |-57| = 57|−57|=57

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

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

Doing the sums and differences inside the absolute values gives

-|6|-|-5|+|-1|-|7|−|6|−|−5|+|−1|−|7|

And now use what I said at the beginning: the absolute value of 66 is 66, the absolute value of -5−5 is 55, the absolute value of -1−1 is 11, and the absolute value of 77 is 77, and thus we have

-6-5+1-7=-17−6−5+1−7=−17

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