Question

How do you simplify `(3/4)abs4 + (-3) – (-1)`?

Answer 1

`(3/4)abs(4)+(-3)-(-1) = 1`

Explanation:

Evaluate the function abs first
Since `abs(4) = 4`
The expression becomes
`color(white)("XXXX")` `(3/4)(4)+(-3)-(-1)`

Evaluate the multiplication next
Since `(3/4)(4) = 3`
The expression becomes
`color(white)("XXXX")` `3+(-3)-(-1)`

Evaluate addition and subtraction starting from the left
Since `3+(-3) = 0`
The expression becomes
`color(white)("XXXX")` `0-(-1)`

Perform the final subtraction
Since `-(-1) = +1`
The expression reduces to
`color(white)("XXXX")` `1`

Answer 2

`(3/4)*|4|+(-3)-(-1)=1`

Explanation:

1.) First, let's look at "the absolute value" of `4`

Recall that "the absolute value" of something is something and "the absolute value" of (negative)something is something:

|something| = something
|-something| = something

So, `|4| = 4`

2.) So, the `(3/4)*|4|` part becomes `(3/4)*4` which is `3`

(Those `4`'s cancel out)

3.) Now, we are left with:

`3+(-3)-(-1)`

The `+(-3)` is just `-3`

because (plus) a (negative)something is (negative)something:

`+(-`something`) = -`something

and the `-(-1)` is just `+1`

because (minus) a (negative)something is (positive)something:

`-(-`something`) = +`something

4.) So, now we have:

`3-3+1`

`3-3` is `0` and we are then left with `1`

So, `1` is our answer (our simplified junk from above)