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 4?
Responses
A Subtraction Property of EqualitySubtraction Property of Equality
B Commutative Property of AdditionCommutative Property of Addition
C Addition Property of EqualityAddition Property of Equality
D Additive Inverse Property
A Addition Property of Equality
The correct answer is D) Additive Inverse Property. In Step 4, we are subtracting 8x from both sides of the equation to eliminate the variable on the left side. This is accomplished by using the Additive Inverse Property, which states that adding the opposite of a number to itself results in zero.
The property that yields Step 4 is the Additive Inverse Property.
The Additive Inverse Property states that for any real number a, there exists an additive inverse -a such that a + (-a) = 0.
In Step 4 of the given sequence of steps, we have 8x - 8x - 12 = 9x - 8x - 36. We can apply the Additive Inverse Property by subtracting 8x from both sides of the equation. This allows us to cancel out the terms with 8x on the left side, resulting in -12 = x - 36.