An equation that has no solution is one that leads to a false statement, that is, a result that is impossible to be true.
For example:
[tex]3(x+5)=3x+11[/tex]If you solve it for x you'll get the following result:
[tex]\begin{gathered} 3x+15=3x+11 \\ 3x-3x+15=11 \\ 15=11 \end{gathered}[/tex]The result of this equality is impossible and has no solution.
The symbol used to indicate that an equation has no solution is ∅
