Hi. when adding equations i.e. 3x = -7x^2+9 which side do I set to zero? I have come across multiple problems where sometimes the left side is set to zero and sometimes the right side is set to zero. Thanks for any help!!
It does not matter (so you do whichever is easier).
In this case we have:
3x = -7x^2+9
so subtracting 3x from both sides we get:
0 = -7x^2 - 3x + 9
or subtracting -7x^2+9 from both sides we get:
7x^2 + 3x - 9 = 0.
These two can then be transformed into one another by switching
the equlities around and multiplying by -1.
Note: 7x^2 + 3x - 9 = 0 is the same thing as 0 = 7x^2 + 3x - 9.
RonL
Be careful with your signs and you should have no problems:
4x + 12 - 5x - 25 = -6x^2 - 48x - 90
First (always) combine like terms:
-x - 13 = -6x^2 - 48x - 90
Now move terms.
If we move the terms to the right, we get
-6x^2 - 48x + x - 90 + 13 = 0
-6x^2 - 47x - 77 = 0 ... multiply everything by -1
6x^2 + 47x + 77 = 0
If we move the terms to the left, we get
6x^2 - x + 48x - 13 + 90 = 0
6x^2 + 47x + 77 = 0
Notice that the two answers became the same (if I multiply one version by -1, that is).
you don't have to multiply by -1 if you don't want to, ecMathGeek was just illustrating it doesn't matter what side you bring everything on, everything will work out to be the same.
also, it's not aesthetic to have a minus in front, so whatever side you decide to solve on, if there is a minus sign in the front, you usually multply by -1 to change it to plus. it does not change the equality to do that
so to answer your question directly, no, it is not always the case that we multiply by -1 if we move to the right, its a matter of convenience and looking good while we're doing math