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How do you evaluate #abs(12-4)-abs(-8+8)-1#?

Answer 1

Jeremiah Andrews

An absolute value is a vertical line with something in the middle that is always positive.

So for example #|-3| = 3#

Thus: #|12-4| = +8#

And: #|-8+8| = +0#

But #-|8-8| = -(|8-8|) = -(+0) = -0#

#color(blue)("Putting this all together")#

#|12-4|-|-8+8|-1" "=" "8-0-1 = 7#

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Answer 2

Gabriel Agustin

To evaluate the expression abs(12-4)-abs(-8+8)-1, follow the order of operations:

Evaluate inside the absolute value bars: abs(12-4) = abs(8) = 8 abs(-8+8) = abs(0) = 0
Substitute the results back into the expression: 8 - 0 - 1
Perform the subtraction: 8 - 0 - 1 = 7

Therefore, the value of the expression abs(12-4)-abs(-8+8)-1 is 7.

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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.