Sanjay solved the equation below. Which property did he use to determine that 7 x + 42 = 42 is equivalent to 7 x = 0?

Question

7 (x + 6) = 42. 7 x + 42 + 42. 7 x = 0. x = 0.
distributive property of equality
subtraction property of equality
multiplication property of equality
division property of equality

Answer 1

To determine which property Sanjay used to transition from the equation \( 7x + 42 = 42 \) to \( 7x = 0 \), let's analyze the steps he took:

1. Start with the equation \( 7(x + 6) = 42 \).
2. Distributing the 7 gives us \( 7x + 42 = 42 \).
3. To simplify \( 7x + 42 = 42 \) to \( 7x = 0 \), Sanjay subtracted 42 from both sides of the equation.

The property that corresponds to the action he took of subtracting 42 from both sides is the subtraction property of equality. Therefore, the correct answer is:

subtraction property of equality.