SOLUTION: 9(2x)=(9 x 2)x Would this problem be commutative, assosiative, identity or a false statement.

Question 113228: 9(2x)=(9 x 2)x
Would this problem be commutative, assosiative, identity or a false statement.
Answer by Edwin McCravy(20077) (Show Source): You can put this solution on YOUR website!



9(2x)=(9 x 2)x

You are using an x for both an unknown and also for 
the multiplication sign.  That makes it confusing.

So I'll use an askerisk * to denote multiplication.

9(2x) then means 9*(2*x)
(9 x 2)x then means (9*2)*x

So the equation you have is

9*(2*x) = (9*2)*x

You are comparing 9*(2*x) with (9*2)*x.

Suppose x represents 3. Then

9*(2*x) = (9*2)*x

means

9*(2*3) = (9*2)*3

The left side of 9*(2*3) = (9*2)*3 is done this way:

We start with 9*(2*3). Then we do what's in the 
parentheses first and change the (2*3) to (6). 

That makes 9*(2*3) become 9*(6)
Then 9*(6) means 9*6 which comes out 54

Now let's do the right side of 9*(2*3) = (9*2)*3:

Starting with (9*2)*3, we do what's in the parentheses 
first and change the (9*2) to (18). 

That makes (9*2)*3 become (18)*3
Then (18)*3 means 18*3 which also comes out to equal 54.

Therefore 9*(2*x) = (9*2)*x is a true whenever x = 3.

Let's pick another number for x to see if it is true
when x is that number.  Suppose we pick 1 for x this
time.

Then

9*(2*x) = (9*2)*x

means

9*(2*1) = (9*2)*1

The left side of 9*(2*1) = (9*2)*1 is done this way:

We start with 9*(2*1). Then we do what's in the 
parentheses first and change the (2*1) to (2). 

That makes 9*(2*1) become 9*(2)
Then 9*(2) means 9*2 which comes out 18

Now let's do the right side of 9*(2*1) = (9*2)*1:

Starting with (9*2)*1, we do what's in the parentheses 
first and change the (9*2) to (18). 

That makes (9*2)*1 become (18)*1
Then (18)*1 means 18*1 which also comes out to equal 18.

Therefore 9*(2*x) = (9*2)*x is a true whenever x = 1.

Let's pick another number for x to see if it is true
when x is that number.  Suppose we pick 87 for x this
time.

Then

9*(2*x) = (9*2)*x

means

9*(2*87) = (9*2)*87

The left side of 9*(2*87) = (9*2)*87 is done this way:

We start with 9*(2*87). Then we do what's in the 
parentheses first and change the (2*87) to (174). 

That makes 9*(2*87) become 9*(174)
Then 9*(174) means 9*174 which comes out 1566

Now let's do the right side of 9*(2*87) = (9*2)*87:

Starting with (9*2)*87, we do what's in the parentheses 
first and change the (9*2) to (18). 

That makes (9*2)*87 become (18)*87
Then (18)*87 means 18*87 which also comes out to equal 1566.

Therefore 9*(2*x) = (9*2)*x is a true whenever x = 87.

So 9*(2*x) = (9*2)*x

must be true no matter what number x is. 

They both involve multiplying three quantities,
9, 2 and x.

In 9*(2*x) the parentheses are ASSOCIATING the
2 and the x together

In (9*2)*x the parentheses are ASSOCIATING the
9 and the 2 together.

So it's the ASSOCIATIVE PRINCIPLE that is being
demonstrated here.

Edwin

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