Explain why the equation 8 x + 19 = 11 has no solution

It has a solution, but it isn't a positive number, it's a negative one (which you probably didn't get to jet at school, so teacher said it hasn't got a solution)

8X + 19 = 11

move every normal number without X to one side (remember, when moving number across sides, change its sign)

8X = 11 - 19

now

8X = - 8

and you get X that is a negative

X = - 8/8

X = - 1