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 7?
Responses
A Additive Inverse PropertyAdditive Inverse Property
B Additive Identity PropertyAdditive Identity Property
C Addition Property of EqualityAddition Property of Equality
D Commutative Property of Addition
C Addition Property of Equality
The property that yields Step 7 is the Addition Property of Equality.
The property that yields Step 7 is the Addition Property of Equality.
The Addition Property of Equality states that if you add the same value to both sides of an equation, the equation remains true. In Step 7, we added 36 to both sides of the equation to isolate the variable x on one side. This step allows us to simplify the equation and find the value of x.