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

1 Answer

Answer:

#-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)#

https://www.ipracticemath.com/learn/algebra/commutative-associative-laws