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?
Additive Inverse Property
Additive Identity Property
Addition Property of Equality
Commutative Property of Addition
Addition Property of Equality
The property that yields Step 7 is the Addition Property of Equality.
Step 7 in the sequence of steps uses the Addition Property of Equality.
The Addition Property of Equality states that if you add the same quantity to both sides of an equation, the equality is preserved. In other words, you can add or subtract the same number from both sides of an equation without changing the solution.
In this case, we added 36 to both sides of the equation to isolate the variable x. By doing so, we were able to simplify the expression on the right side of the equation and obtain the solution of x = 24.