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

Answer 1

#-17#

The absolute value of a positive number is the number itself; the absolute value of a negative number is the positive version of that number. In formulas: Just keep in mind that the absolute value always returns the positive version of the number it contains inside of it.

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

Let us now examine the contents of your absolute values: your equation is

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

Adding up and subtracting within the absolute values yields

#-|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#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eli Assouline

To simplify the expression, first evaluate each absolute value separately, then subtract the values from each other:

|-6| - |-5| + |7| - |7|

This simplifies to:

6 - 5 + 7 - 7

Then, perform the arithmetic:

6 - 5 + 7 - 7 = 1

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.