Question

select the correct answer.
what is the justification for step 2 in the solution process?
12y - 40 - 4y = 6y - 18
step 1: 8y - 40 = 6y - 18
step 2: 2y - 40 = -18

a. the subtraction property of equality
b. the multiplication property of equality
c. the division property of equality
d. the addition property of equality

Explanation:

To determine the justification for Step 2, we analyze the transformation from Step 1 (\(8y - 40 = 6y - 18\)) to Step 2 (\(2y - 40 = -18\)). We subtract \(6y\) from both sides of the equation. The subtraction property of equality states that if we subtract the same quantity from both sides of an equation, the equation remains true. Here, subtracting \(6y\) from both sides (equivalent to subtracting \(6y\), which is a subtraction operation) leads to the new equation. The multiplication or division properties involve multiplying or dividing both sides by a non - zero number, and the addition property involves adding a quantity, so they do not apply here.

Answer:

A. the subtraction property of equality