How do you simplify #abs((-(3-1)+5)div(-2))#?

Answer 1

#3/2#

#color(blue)("Introduction to concept")#
The | | turns what ever is inside it into a positive value. AS an example: #|-7|=|+7|=7#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Consider: "color(green)((-color(red)((3-1))+5)#

Bracket within brackets is called nested brackets. In this situation you consider each pair of brackets working outwards

Step 1: #" "color(red)((3-1) = +2)#
Step 2: #" "color(green)((-color(red)((3-1))+5)" "->" "color(green)((-color(red)((+2))+5)#
#" "->" "(-2+5) = (+3)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#|color(white)(.)(-(3-1)+5)-:(-2)color(white)(.)|" " =" " |color(white)(.)3-:(-2)color(white)(.)|#
#" "=" "|color(white)(.)-3/2color(white)(.)|#
#" "=" "+3/2#
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Answer 2

#3/2#

A number's absolute value is always positive, but before we can calculate its absolute value, we must first simplify its contents. Let's do that now:

#abs((-(3-1)+5)-:(-2))#

First, it's a little hard to see what's going on, so to help a little, I'll add some color. Specifically, I'll color a term that is inside brackets and needs to be completed before we can complete the division (which is the operation that initially caught my attention):

#abs(color(green)((-(3-1)+5))-:(-2))#

Thus, I will complete the green portion independently and then return the result:

#color(green)((-(3-1)+5))=(-(2)+5)=(-2+5)=(3)#

Let's now return the solution to this section to the original:

#abs(3-:(-2))=abs(-3/2)#

then we are able to obtain the absolute value:

#abs(-3/2)=3/2#
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Answer 3

To simplify the expression abs((-(3-1)+5) ÷ (-2)), follow the order of operations (PEMDAS/BODMAS):

  1. Simplify the expression inside the parentheses: -(3 - 1) = -2

  2. Add 5 to the result: -2 + 5 = 3

  3. Divide the result by -2: 3 ÷ (-2) = -1.5

  4. Find the absolute value of the result: abs(-1.5) = 1.5

Therefore, the simplified expression is 1.5.

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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.

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.

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.

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.

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