Consider the sequence of steps to solve the equation:
5(x-3)=7x/2
Step 1 = 10(x - 3) = 7x
Step 2 = 10x - 30 = 7x
Step 3 = 3x - 30 = 0
Step 4 = 3x = 30
Step 5 = x = 10
Identify the property of equality which gets us from Step 3 to Step 4.
A. Division Property
B. Addition Property
C. Subtraction Property
D. Multiplication Property
C. Subtraction Property
The property of equality that gets us from Step 3 to Step 4 is the addition property.
The correct answer is C. Subtraction Property.
To solve the equation, we used the Subtraction Property of Equality to simplify the equation from Step 3 to Step 4.
In Step 3, we have the equation 3x - 30 = 0. To isolate the variable x, we need to get rid of the constant term -30. We achieve this by applying the Subtraction Property of Equality, which states that we can subtract the same quantity from both sides of an equation without changing its solution.
By subtracting -30 from both sides of the equation in Step 3, we get 3x = 30 in Step 4. This allows us to continue simplifying the equation and solving for the value of x in the subsequent steps.