The next puzzle is x+4=x. What is the value of x.
This is a lesson in observation. It’s making sure you notice that it’s a plus not a times, an addition not a multiplication.
But here’s the thing: I really had no idea how to solve this and after three guesses (zero, 1, -4) I gave up. So when I did, I felt a sense of deja vu, back to the crowded schoolroom when everyone else got it (or claimed to) while I sat thinking I was thick. So imagine my reaction when, after my failure, up pops a message saying ″There doesn’t seem to be any solution to this equation.
It’s worth a few minutes to look at the lesson at https://schoolyourself.org/learn/algebra/no-solution
Far from being cross and seeing my time as wasted, I take this as the reason for the white hole. We need somewhere to put things that we cannot answer.
It was especially not wasted when I got to the page that says ″for which of these equations are all numbers solutions.″ The lesson here, for me, was not in the maths: it was in the English and, in particular, the fact that a) I didn’t read it properly and b) there’s a buzzword that I didn’t realise was a buzzword. Also, the narrator emphasises the wrong word: ″numbers″ when the emphasis should be on ″all″ if it’s to make sense.
I assumed that the solution would be all numbers and therefore I had to solve it by removing the letters. Zero success. Get hint. That’s when I discovered that what was intended was that I would find a solution where the equation was solved no matter what value I gave to the variable. In short, all numbers, not all numbers, solve it.
We’ll get back to that later, too, in the conclusion to this piece.
But here’s a hint: there is far more connectivity and dependence between maths and language than we might imagine. And if you want to get the right answers, you have to have information in a form that makes sense – and doesn’t undermine comprehension.