Question 886195: Hello, I have come across an equation in my algebra that I cannot get the correct answer to. Here is the equation:
6(x-2)-3(x+1)=4(3+2)
The book's answer is that x=35/3 (The answer I need to get is that x equals thirty-five thirds)
The answer that I constantly come up with is that x=29/3
I recently came across this website and tried the Universal Simplifier and equation solver. After doing so I found out that there was no typo in my algebra book, and that the correct answer actually was that x = 35/3. I started looking at the steps to see what I did wrong, but I do not understand a particular one. Here is the step that confuses me, quoted from how this website puts it.
Look at: 6*x-3*(x+1)-32=0
Expanded term -3 by using associative property on {x+1}
It becomes: 6*x-3*x-3*1-32=0
Their solution uses the associative property of multiplication, but not in a way I am familiar with. I consider the proper way to do this method is that a(b+c) = a(b)+a(c)
They assumed that the first number/variable (represented by a) was negative because there was a - symbol behind it. Thus, it worked out to be:
-a(b+c)=-a(b)+-a(c)
This means that both b and c would be negative variables/numbers. This DOES make sense, until you realize that this is also a subtraction problem in the entire equation. If there were a - symbol there, that would mean ONE of two things: the number in the problem is negative OR you do the multiplication then subtract the result. The method given seems to do BOTH. The result of the first number being -3 makes the result of this multiplication problem: -3x-3
Now, let's put that back into the equation 6*x-3*(x+1)-32=0 :
6*x(-3x-3)-32=0
This now indicates that you are to perform 6x times the variable (-3x-3), correct?
I guess what I'm wanting to know is what to do in this step and exactly why it is done this way. Thank you very much for your time,
Abe
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 6(x-2)-3(x+1)=4(3+2)
law of operations says do multiplication and division first from left to right, then addition and subtraction from left to right. note that parenthesis says do me first. here we go
6x-12 -3x-3 = 20
combine terms
3x -15 = 20
add 15 to both sides of =
3x = 35
divide both sides of = by 3
x = 35/3
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