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1/3(x + 9) = 12

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    The question is 1/3 ( x + 9 ) = 12.  You want to find out the value of x.

The way I sometimes teach the idea behind solving an equation is to first walk through it step-by-step in words:

1. This statement is telling you that one-third of the value of x + 9 is equal to 12.  Let's call x + 9 an expression.


2. If one third of any expression is equal to 12, then the entire expression must be equal to 36 (because you need three thirds to get to a whole, and 3 times 12 will get you to 36, won't it?)  So now we've gotten rid of the 1/3 part and can just say x + 9 is equal to 36.


3. If 9 and something is equal to 36, we can take 9 away from 36 to find out what that is (real quick, take ten away from 36 and then add one back).


4. The answer is 27.  x = 27.

You need to do the reciprocal of 1/3 and multiply it to the other side. That will give you 36. so your equation will look like this x+9=36. Then subtract the 9 from the 36. And you will get x=27.

You can check your answer by plugging in the 27 in the original equation. 1/3((27)+9)=12. Your answer will be 12=12 which indicates that your answer is correct!

 


Hope this helps! :)

 

The best way to approach this is to get rid of your fraction.

So first you want to multiply both sides by the reciprocal of 1/3, which is 3. 

This leaves you with (x+9)=36.

From there you can subtract 9 from both sides and you have x+9-9=36-9, or x=27

Solving for x:

1/3(x + 9) = 12

multiply both sides by 3 to remove the denominator:

(3)(1/3(x + 9)) = (3)12

(x + 9) = 36

subtracting 9 from both sides:

x + 9 - 9 = 36 - 9

x = 27

Two ways you can do this

1) multiply 1/3 through the parentheses on the left side

1/3(x+9) = 1/3x +3 = 12

1/3x +3 -3 = 12 -3

1/3x =9

x=27

or you can multiply by 3 on both sides

3*(1/3)(x+9)=12*3

x+9 = 36

now subtract nine from both sides

x+9 -9 =36-9

x=27

Check for correctness

1/3(27+9) = 12

1/3(36) = 12

12 = 12