SOLUTION: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

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Question 147147: How do you know when an equation has infinitely
many solutions? How do you know when an equation has no solution?
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
--When one side of an equation is identical to the other side, then there is an infinite number of solutions. for example x=x. Whatever you plug in for x will work. Or 4x+4x=8x. You would end up with 8x=8x, so any value for x is appropriate. basically, if you see that the equation is already true without having to find what value for x makes it true, then all values for x will work. This means that the equation has an infinite number of solutions.
--If you have an equation and you end up with unequal values on each side of the equation (oxymoron there!), then there is no solution. Basically, if the equation is no longer an equation, there is no solution. For example 17%2B2x-7=4x%2B3-2x. Once you combine like terms, you get 2x%2B10=2x%2B3. Right away you see that that is not possible. You will end up with 10=3. Therefore there is no solution to this problem, and all problems like this one.