Question

How do you solve 9 (x + 3) = 27 using the distributive property?

Answer 1

Hint: We will first use the distributive property then, we get a new equation altogether and then we do the required modifications to get the required answer.

Complete step-by-step answer:
We are given that we need to use distributive property to solve the equation given by the expression: 9 (x + 3) = 27.
Let us discuss distributive property for one, what it says:-
Distributive Property: For any random real number x, y and z, we have the following equality:
$ \Rightarrow $z (x + y) = zx + zy
Now, if we replace z by 9, x by x only and y by 3 only, we will get:-
$ \Rightarrow $9 (x + 3) = 9x + 9(3)
Simplifying the multiplication on the right hand side of the above equation, we will then get:-
$ \Rightarrow $9 (x + 3) = 9x + 27
Now, we will put it equal to the right hand side as given in the question to us, we will then obtain:-
$ \Rightarrow $9x + 27 = 27
Taking the 27 from addition in the left hand side to subtraction in the right hand side to obtain the following expression:-
$ \Rightarrow $9x = 27 – 27
Simplifying by doing the given calculations on the right hand side, we will then obtain the following expression:-
$ \Rightarrow $9x = 0
Now, divide both of the sides by 9 to obtain the following expression:-
$ \Rightarrow $x = 0

Hence, the answer is x = 0.

Note:
The students must note that in the last few steps we used the fact that if we divide 0 by any real number, we always get 0 as the answer because anything multiplied by 0 gives 0.
The students must notice that if in the question, it was not mentioned that you need to use distributive property, then we would have done it like the following:-
Step 1: Divide both the sides of 9 (x + 3) = 27 by 9 to obtain: x + 3 = 3
Step 2: Now, subtract 3 from both sides to get: x = 0.