What would be an example of a linear equation in one variable with no solution and how would you know there's no solution

Linear Equation in one variable with no solution:

Linear equations also named as first-degree equations in one variable specifies the type of equations in which only one variable is present. Standard form of linear equation in one variable is:

where,  

a, b and c are real numbers and

Example of a linear equation in one variable is:

On solving it we find out that both 5x cancel out and the left over equation is which is false.

In order to check whether an equation has a no solution, check whether the condition holds true or false after simplifying.