Question

Simplify the expression (4x+8)+(-6x). Explain how the associative and commutative properties were used to solve the expression?

Answer 1

`-2(x -4)`

Explanation:

1. use the distribution property to change `+ xx (-6x)` to -6x # ( + xx - = -)#
2. remove the parenthesis giving 4x +8
   ( there are several ways to proceed from here my choice is)

3. use the commutative property to move the +8 and - 6x
   `+ 4x + 8 -6x = 4x - 6x +8` commutative property

4. Use the associative property to group + 4x -6x
   `+ 4x -6x +8 = ( +4x -6x) +8` associative property

5. Use algebraic addition to solve for `( +4x -6x)`
   `(+ 4x -6x) +8 = -2x +8`

6. Use the reverse distribution principal to simply and remove common terms

`-2xx{(-2x)/(-2) + 8/(-2)}= -2( x - 4)`