Since I am new to the algebra and do not fully understand it, I am not sure how to answer the following question. Hope you can help. thanks

Question

how do you know when an equation has infinitely many solutions

Answer 1

If after performing all valid steps, your variable terms all cancel and you end up with something like
0=0, or 8=8, that is, a true statement,
then you have an infinite number of solutions.

if after all variable terms drop out, you are left with a false statement, there is no solution.

e.g.
2x + 6 = 2(x+3+
2x +6 = 2x + 6+0=0 .....true ---> infinite number of solutions.

e.g
2x+6 = 2(x+5)
2x+6 = 2x+10
0 = 4 .... false ---> no solution

Answer 2

clearly a typo, should be

2x + 6 = 2(x+3)
2x +6 = 2x + 6 .....true ---> infinite number of solutions.