No solution: When the solution you get from an equation is false, this means that there is no solution and no value of x will satisfy the equation.
Ex: [tex] 6x-5=6x+17\\ -5=17 [/tex] Since -5 does not equal 17, this is an equation with no solution.
Undefined: When you cannot define an answer mathematically, it's considered an undefined solution. A common example is dividing by zero. Any number, lets take 12, divided by zero would be undefined because there is no number times zero that would equal to 12.
Ex: [tex] \frac{12}{0} [/tex]
Infinite Solutions: When any value of x will satisfy the equation.
Ex: [tex] 6x+5=6x+5\\ 6x=6x\\0=0 [/tex] Because 0 = 0 is a true statement, you are able to plug in any number into the equation.
