Question

How do you simplify `-|7 + 1| - |4 - 8| + |-2 -6| - |3 - 6|`?

Answer 1

Simplify what's inside the absolute value signs, then solve to get `-7`

Explanation:

The absolute value brackets will take the answer within them and make the answer positive. There are 4 brackets in this question so let's do the math within them, change the sign from negative to positive where needed, then do the rest of the math.

Starting from the original:

`-|7+1|-|4-8|+|-2-6|-|3-6|`

First we do the math within the brackets:

`-|8|-|-4|+|-8|-|-3|`

Now we take the absolute value of each bracket:

`-8-4+8-3`

Note that the absolute value doesn't change the math operation outside of it - so for instance in the first term, we took the absolute value of 8 and got 8. The fact that there is a negative sign outside of the absolute value sign is ok - and that's how we end up with `-8`.

Ok - let's now do the final bit of math to clean up the expression:

`-8-4+8-3=-7`