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

Question

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

Kennedy Adams · Accepted Answer

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

The four absolute value brackets in this question are going to take the answer within them and turn it into a positive value, so let's do the math inside of them, flip the sign from negative to positive when necessary, and then finish the calculation.

Initially, let's look at the original:

Number-|7+1|-|4-8|+|-2-6|-|3-6|#

The math inside the brackets is done first:

Eight|-|-4|+|-8|-|-3|#

We now take each bracket's absolute value:

#8-4+8-3#

The fact that there is a negative sign outside of the absolute value sign is acceptable, which is how we arrive at #-8#. Take note that the absolute value does not alter the math operation outside of it. For example, in the first term, we took the absolute value of 8 and got 8.

Alright, let's perform the last calculation to simplify the expression:

#8-4+8-3=-7#

Julia Adams · Answer

undefined To simplify the expression, follow the order of operations: first evaluate the absolute values, then perform addition and subtraction.

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

Now substitute these values back into the expression:

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

-8 - 4 + 8 - 3

Combine like terms:

-8 + 8 - 4 - 3

0 - 4 - 3

-4 - 3

-7