Question

An equation is shown below: 4(x − 3) − 5(x + 1) = 3 Which of the following algebraic properties is not needed to solve this equation? Distributive property Addition property of equality Commutative property of addition Transitive property

Answer 1

Distributive property YES: 4(x - 3) = 4x - (4)(3)

Addition property YES:
4x - 12 - 5x - 5 = 3
-x - 17 = 3
(-x - 17) + 17 = 3 + 17
-x = 20

Commutative property YES:
4x - 12 - 5x - 5 = 3
4x - 5x - 12 - 5 = 3

Transitive property NO:
if a = c and b = c then a = c