Here’s a thought: start the lesson with "Ten is not equal to zero, ergo this equation has no solutions. However some people who don't understand math might insist that they can get an answer one way or another. I will now show six possible methods for arriving at an answer, and that none of them work."

In programming, due to the Von Neumann architecture, that equation has always a solution, either a primitive value or a symbol representing the absence of a value. It happens that in programming that statement isn't a equation nor an equality, but an attribution statement where time plays its role. For an initial value of x, lets say x1=20, the resulting value will be x2=30. The programming language reads the existing memory's value  of x, 20, sums 10 to it and stores the resulting  value, 30, under the same variable name x. I use this example to show my students that mentally processing a program or algorithm it's not the same as reading the math solution of a math problem.

Three solutions are from transmathematics: infinity, minus infinity, and nullity.

What a comedy to try to calculate on this!
The equation says: If you add 10 to a number the number is unaltered. Clearly nonsense, of course.

Solve an equation that has no solution!
Brilliant.
Mind your decisions would feel jealous.

In the extended real number system, x = ±∞ are solutions, since ±∞ + 10 = ±∞

Plus minus Infinite ist the Solution

Wenn x aus R und x aus C sein kann, dann kann x auch aus {0, 1, 2, 3, 4... 9, 10}
sein..
und dann gilt bekanntlich x + 10 = x für alle x ≠ 0 ;-)

😂

Wow this guy "solves" the same problem in 20 variations in 50 videos. Idiotic

I could beat you in time

x+10=x
{x≠0}
x/x+10/x=x/x
1+10/x=1
10/x=0
x-->±oo
No Solution.

Ans: x ∈ { y | y ≡ x mod 10 }.

x+10 = x
x+10-x = x-x
10 = 0