Question

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

Answer 1

`3/2`

Explanation:

The absolute value of a number is always positive, but before we can do the absolute value, we need to simplify what is inside of it. So let's do that:

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

The first thing I'm seeing is that it's a bit difficult to see what is going on, so I'll add some colour and help things a bit. Specifically, I'm going to colour a term that is within brackets that needs to be done before we can so the division (which is the operation that jumped out at me at first!):

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

So I'm going to do the green section separately, then put the result back in:

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

and now let's put the solution to this part back into the original:

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

and now we can take the absolute value:

`abs(-3/2)=3/2`

Answer 2

`3/2`

Explanation:

`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`