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how do you solve:5/6(6x+12) + 1 = 2/3 (9x-3) +5

how do you solve:
5/6 (6x+12) + 1 = 2/3 (9x-3) +5   these are FRACTIONS not division and I am LOST

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Here is a verbal explanation.
 
Let's do the left side first.  The whole entity (6x+12) must be BOTH multiplied by 5 AND divided by 6.  It doesn't matter which you first, since they are reciprocal operations when performed on the same entity.  So let's get rid of the 6, simply because it is easier (looking at the 6 and 12 in the enclosed entity). That leaves us with x+2.  5 times that?  5x+10.  Oh wait... we have a +1 to add to this.  Since that is like saying 5x+10+1... well, that's just like saying 5x+11 isn't it?  There it is for the left side.
 
Now the right side...  doing it the same way we have 9x-3 getting divided by three, which leaves us with 3x-1. Times two? 6x-2.  Add 5 and that makes it 6x+3.
 
 So it looks like they are saying 5x+11 = 6x+3.  Is there any number "x" which makes this true?  We only need one.  In fact there is only one real number which can make this true!  All we have to do is subtract one side from the other to find out what it is!
 
Let's do something to both sides.  That's fair, since if both sides are equal I should be able to do what I want to both sides, as long as it's the same thing, and they'll still be equal.
 
Let's subtract the left from the right, since it will leave x by itself on the right in positive form, and the left will be zero (since it was subtracted from itself!).  That gives us 0=x-8.
 
Let's get rid of that -8.  How?  Just add 8 to both sides!  That cancels out the -8 leaving only x on that side, and puts a positive 8 on the other.  It appears now that 8=x.  Or, by the reflexive property, x=8.

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1 Answer

Multiply both sides by LCD = 6,
5(6x+12) + 6 = 4(9x-3) + 30
Simplify by collecting variables in one side and numbers in the other side,
6x = 48
 
Answer: x = 8

Comments

can you show me the problem so I can see each side. I am getting stucl around the 3rd level....
 
5(6x+12) + 6 = 4(9x-3) + 30
30x+60+6 = 36x-12+30
Take 18 away from both sides,
30x + 48 = 36x
Take 30x away from both sides,
48 = 6x

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