Question

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

Answer 1

`-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`