Question

Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36 Given ⇒ 3(x − 4) + 5x = 9x − 36

Step 1 ⇒ 3x − 12 + 5x = 9x − 36
Step 2 ⇒ 3x + 5x − 12 = 9x − 36
Step 3 ⇒ 8x − 12 = 9x − 36
Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36
Step 5 ⇒ 0 − 12 = x − 36
Step 6 ⇒ −12 = x − 36
Step 7 ⇒ −12 + 36 = x − 36 + 36
Step 8 ⇒ 24 = x + 0 Step 9 ⇒ 24 = x
Which property yields Step 1? A) Distributive Property B) Multiplicative Identity C) Multiplication Property of Equality D) Commutative Property of Multiplication

Answer 1

A) Distributive Property.

Explanation:

The distributive property is a(b + c) = ab + ac . Here we have 3(x - 4) = 3x - 12.