Question

How can you use the order of operations to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x + 5) - x = 42

Answer 1

Answer:

Step-by-step explanation:

The distributive property tells us that the term in the inside the parentheses will by multiply by the term on the outside of the parentheses first.  Example:

3(x + 5) means that (x + 5) + (x + 5) + (x + 5) = 3x + 15

So 7(x + 5) - x = 42 ; without the distributive property you would have to write what is inside the parentheses seven times then complete solving the problem

7( x + 5) -x = 42

(x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) - x = 42   by definition

(x + x + x + x + x + x + x) + (5 + 5 + 5 + 5 + 5 + 5 +5) -x = 42  (x + 5) Associative and Commutative

7x + 35 - x = 42      Addition

6x + 35 = 42           Associative and Commutative

6x = 7                     Subtraction

x =7/6                     Division

Now with the Distributive property

7(x + 5) - x = 42

7·x + 7 · 5 - x = 42        Distributive property

7x + 35 - x = 42           Multiplication

6x + 35 = 42                Associative and Commutative

6x =  7                          Subtraction

x = 7/6                          Division