There's no variable left, so I don't know what to write as my answer.
Accepted answer
The variable vanishing is itself the answer — which one depends on whether what's left is true.
**`0 = 5` (a false statement) → no solution.** You've shown that assuming a solution exists leads to nonsense, so nothing satisfies the equation. Write "no solution" or `∅`. Graphically: two parallel lines that never meet.
**`0 = 0` (a true statement) → infinitely many solutions.** The equation is true for every value; the two sides were the same expression in disguise. Write "all real numbers." Graphically: the same line twice.
For example `2x + 3 = 2x + 7` subtracts to `3 = 7` — false, no solution. But `2x + 3 = 2(x + 1) + 1` simplifies to `2x + 3 = 2x + 3`, so `0 = 0` — every real number works.
The mistake to avoid is writing `x = 0`. There is no `x` in `0 = 5`; the variable is gone, not zero.