Posted by lilmissluck on .
o How do you know when an equation has an infinite number of solutions?
o How do you know when an equation has no solution?

algebra 
Reiny,
If after you perform all proper steps and simplifications, the variables drop out and you end up with a TRUE statement, then there is an infinite number of solutions.
If after you perform all proper steps and simplifications, the variables drop out and you end up with a FALSE statement, then there is no solution.
e.g.
(x+1)^2 = x^2 + 2x + 1
x^2 + 2x + 1 = x^2 + 2x + 1
1=1 true, thus infinite numer of solutions
e.g.
3(2x + 5) = 6x+1
6x + 15 = 6x+1
15 = 1  false, therefore no solution.