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

Jul 14, 2018

$- 2 \left(x - 4\right)$

#### Explanation:

1. use the distribution property to change $+ \times \left(- 6 x\right)$ 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
$+ 4 x + 8 - 6 x = 4 x - 6 x + 8$ commutative property

4. Use the associative property to group + 4x -6x
$+ 4 x - 6 x + 8 = \left(+ 4 x - 6 x\right) + 8$ associative property

5. Use algebraic addition to solve for $\left(+ 4 x - 6 x\right)$
$\left(+ 4 x - 6 x\right) + 8 = - 2 x + 8$

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

$- 2 \times \left\{\frac{- 2 x}{- 2} + \frac{8}{- 2}\right\} = - 2 \left(x - 4\right)$