Question

what is the justification for step 2 in the solution process?
12 - x = 7x + 32
step 1: -x = 7x + 20
step 2: -8x = 20
a. the multiplication property of equality
b. the subtraction property of equality
c. the addition property of equality
d. the division property of equality

Explanation:

To determine the justification for Step 2, we analyze the transition from Step 1 ($-x = 7x + 20$) to Step 2 ($-8x = 20$). We subtract $7x$ 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 $7x$ from both sides ($-x - 7x = 7x + 20 - 7x$) simplifies to $-8x = 20$, which matches the operation in Step 2. The multiplication property involves multiplying both sides, the addition property involves adding, and the division property involves dividing—none of these match the subtraction of $7x$ here.

Answer:

B. the subtraction property of equality