How Do You Solve for x in This Algebra Equation?

[haengbon]

I'm not sure it is the correct thread, but it did say Algebra homeworks could be posted here too right?

Homework Statement

3bx - ab + 2a^2 = 2ax + 3b^2

solve for the x.

Homework Equations

none

The Attempt at a Solution

3bx - ab + 2a^2 = 2ax + 3b^2
2a^2 - 3b^2 = 2ax - 3bx + ab
2a^2 - 3b^2 = x(2a - 3b) + ab
2a^2 - 3b^2 -ab = x(2a - 3b)

after which, I'm, stuck I don't know what to do anymore, nor do I know if I'm dog it right! my book says, the answer should be x=a+b. sadly, it doesn't give an explanation as to how it got the answer please help? I really need to pass my exam two days from now, and solution sets is a big part of it.

 

[CompuChip]

You could try writing the left hand side as (2a - 3b) ( ... ) and divide out (2a - 3b) (provided it is not zero).

 

[Zayer]

First, put the terms with x on one side and the rest on the other side.Then, factor x out and divide both sides to have the x alone on one side.Finally,simplify.

 

[thebigstar25]

I can understand your struggle when you have the answer but you don't know how they get there, anyway I have much simpler way to do it .. you reached to a good step .. so all what left is to perform a division.. I made a figure illustrating the idea .. just go with me step by step :


http://img189.imageshack.us/img189/9431/11291260.jpg

as you can see it is just a long division but this time it is with two variables .. so how to do it?

well,

first : take a as your variable and anything else as constant (check the red colored writing) divide 2a with 2a^2 put the result up (which is a ) then multiply it with 2a - 3b and write it below 2a^2 - 3b^2-ab (each result below the one that looks similar to it)

second : take b as your variable and anything else as constant (check the blue colored writing) divide -3b with -3b^2 and put the result up (which is b) then multiply it with 2a - 3b and write the result below 2a^2 - 3b^2 -ab ( also put each result below the one that looks similar to it)

thired : change the sign of all the previous results (check the green colored writing) and add every thing , you will end up with zero with tells you that when you divide 2a^2 - 3b^2 -ab with 2a-3b that will give you a+b with no reminder ..

I hope now you got it :) .. and good luck with your test ..

 

[ehild]

You can rewrite the left side as

2a^2-2b^2 -b^2-ab= 2(a^2-b^2)-b(b+a)=
=2(a-b)(a+b)-b(a+b)= (a+b)(2a-2b-b)=(a+b)(2a-3b)

So the equation becomes: (a+b)(2a-3b)=x(2a-3b)

Divide both sides by 2a-3b (supposing it is not 0) the result is x=a+b.
If 2a-3b=0 any x is solution.

ehild

 

[CompuChip]

So, the four of us have now provided you with the complete answer :)

 

[haengbon]

ohmy :) thank you thank you thank you! I'm glad all of you have responded