Question

When given an equation how can you determine if it will have no solution

Answer 1

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:

`3(x+5)=3x+11`

If you solve it for x you'll get the following result:

`\begin{gathered} 3x+15=3x+11 \\ 3x-3x+15=11 \\ 15=11 \end{gathered}`

The result of this equality is impossible and has no solution.

The symbol used to indicate that an equation has no solution is ∅