Question

How do you use order of operations to simplify `3(-2) +6 -(-2) - 5`?

Answer 1

Order of operations

1. Parentheses
2. Exponentiation
3. Multiplication and Division
4. Addition and Subtraction
   (Left to right for operations at the same level)

This is sometimes simplified as
PEDMAS but this can be misleading since
Division and Multiplication are at the same level
and
Addition and Subtraction are at the same level
(and it doesn't acknowledge the Left to Right rule)

For the given expression
`3(−2)+6−(−2)−5`

1. There is no simplification of values within parentheses
2. There are no exponents
3. There is one multiplication: `3(-2) = (-6)`, so the expression now becomes `(−6)+6−(−2)−5`
4. All remaining operations are at the "Addition and Subtraction Level" and must be performed Left to Right

4.a `(-6)+6 = 0` and the expression becomes `0-(-2)-5`
4.b `0-(-2) = 2` and the expression becomes `2-5`
4.c `2-5 = -3`

`3(−2)+6−(−2)−5`
`=(−6)+6−(−2)−5`
`=0-(-2)-5`
`=2-5`
`= -3`

Answer 2

`-3`

Explanation:

Count the number of terms first and simplify each term to a single number.

Add or subtract the answers in the last step.

`color(magenta)(3(−2))color(blue)(+6)color(green)(−(−2))color(red)(−5)" has 4 terms"`

=`color(magenta)(-6)color(blue)(+6)color(green)(+2)color(red)(−5)`

=`-3`