Question

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 yields Step 5.
I'm thinking division.

Answer 1

Division Property of Equality

Explanation:

→In Step 4, it is shown that the equation is:

3x = 30

→However, to solve for x, you must get it by itself. This means you need to get rid of the 3 that's being multiplied. So since the 3 is being multiplied to x, you must do the opposite of multiplication, which is division.

→As you can see, the total of 30 is decreased in Step 5, since it has been divided by 3, giving you a total of 10.

This shows that the property of equality that yields Step 5 is the Division Property of Equality.