I have a bunch of algebra problems and I cannot figure out how to do them - it seems sometimes you start by adding numbers, sometimes subtracting... is there some formula or rule to do problems like these - ? Thanks in advance for any help.
6+3x=-5x+62
-5x+3=-74+6x
-1+x=3x-11
-3x-1=5x+71
Hi. Most of the time, you have a choice of how to proceed.
To solve linear equations like these, we need to combine like-terms. We need to get all of the variable terms (i.e., those containing a factor of x) to one side of the equation and all of the constant terms to the other side.
Here's an example:
4x - 10 = -2x + 1
I decide to put the variable terms on the left and constant terms on the right. (If I were to choose to do the opposite, I would still get the same answer.)
I add 2x to each side because this will get rid of the -2x on the right.
4x - 10 + 2x = -2x + 1 + 2x
6x - 10 = 1
Now there's one variable term, and it's on the left. Next, I want the constants to be on the right. To get rid of the -10 on the left, I add 10 to each side.
6x - 10 + 10 = 1 + 10
6x = 11
I have the variable terms (combined) one one side and the constants (combined) on the other, and so now I can solve for x, by taking 1/6th of each side (that is, dividing each side by 6).
(1/6)(6x) = (1/6)(11)
x = 11/6
Again, the main point is to separate the x-terms and the constants to opposite sides of the equation. There's more than one way, and you get to choose which way. Questions?
Here's your first exercise:
6 + 3x = -5x + 62
You can choose to subtract 3x from each side (the variable term will end up on the right), OR you can add 5x to each side (the variable term will end up on the left). Either way, try it.
