With a tidy equation like 5x − 3 = 2x + 9, x lives on both sides. That means verifying isn't "work out one side" — it's work out the left side, work out the right side, and check the two numbers are equal.
Both Sides, Separately
Say someone claims x = 4. Substitute into the left: 5×4 − 3 = 20 − 3 = 17. Now the right: 2×4 + 9 = 8 + 9 = 17. Both give 17, so x = 4 is genuinely the solution. The key move is keeping the two sides apart — you're not solving again, you're comparing two finished numbers.
The Near-miss Trap
Here's where people slip. Try x = 5 instead: left side 5×5 − 3 = 22, right side 2×5 + 9 = 19. Close — only 3 apart — but not equal, so x = 5 is wrong. A near-miss value can look believable, especially if you rushed the solving. Press "surprise me" in the toy: it often hands you an answer that's off by one. Substitution is the lie detector — the sides simply won't match.
Catching Your Own Slips
The same check guards against arithmetic mistakes you make while verifying. If you fumble a negative — say you do 5×4 − 3 = 23 by accident — the sides won't agree and you'll redo it. So verification protects you twice: once from a wrong solution, and once from a wrong check. Slow down on the negatives, do each side fully, and let the comparison be the judge.