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 6? A) Additive Inverse Property B) Additive Identity Property C) Addition Property of Equality D) Commutative Property of Addition

Answer 1

Answer:

B) Additive Identity Property.

Step-by-step explanation:

Let us consider the definition of Additive Identity Property:

The additive identity property states that if you add a real number to zero or add zero to a real number, then you get the same real number back. The number zero is known as the identity element, or the additive identity.

In Step 5 we can see that,

$0-12 = x - 36$

In Step 6 we get,

$-12= x-36$

So basically, $0-12 = -12$

We know that $-12$ is a real number and if a real number is added to 0, we get the real number back, so in step 6 we got -12.

Therefore, additive identity property yields step 6.