Question

How do you evaluate `|9+ - 12+ 5+ - 8|`?

Answer 1

`|9+(-12)+5+(-8)| = 6`

Explanation:

First evaluate whatever is inside the absolute value symbols.

As far as PEMDAS, there is only addition and subtraction, so just move from left to right.

`|color(red)(9+(-12))+5+(-8)| color(white)"XXX"` Add the first two terms together.
`|color(red)((-3)) + 5 + (-8)|`
`|color(orange)((-3) + 5) + (-8)| color(white)"XXXX"` Now add that number to the next term.
`|color(orange)(2)+(-8)|`
`|color(limegreen)(2+(-8))| color(white)"XXXXXXXXX"` Now add that number to the next term.
`|color(limegreen)(-6)|`

`color(blue)(|-6|) color(white)"XXXXXXXXX"` Finally, take the absolute value of this number.

The absolute value of a number is just its distance (how far away it is) from `0`.

Even though `color(blue)(-6)` is negative, distance cannot be negative, so we say that `color(blue)(-6)` is a distance of `6` away from `0`.

In other words,
`color(blue)(|-6|) = 6`

So the final answer is `6`.

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(Remember, absolute value is never negative, since it is the distance from zero. Absolute value of a positive number is just that number, and absolute value of a negative number is that number with a positive sign instead of a negative sign.)