Question

HOW DO YOU KNOW WHEN AN EQUATION HAS INFINITELY MANY SOLUTIONS AND WHEN AN EQUATION HAS NO SOLUTION??

Answer 1

If after you have followed all the correct steps of solving the equation, the variable terms have all dropped off, look at the final statement.

if the statement is true, e.g. 2 = 2, then there is an infinite number of solutions.
If the statement is false , e.g. 4 = 0, then there is no solution.