That depends a lot on what exactly you want to check. For example:* You can check a division, by doing the corresponding multiplication.
* You can check the solutions to an equation, by replacing the variable with the purported solution and doing the calculations.
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You could try substituting the solution into the original question and check whether it is valid.
Mathematically you check your solution to make sure you have the correct answer. In some cases the slightest miscalculation could cause a disaster or you could end up with low marks in schoolScientifically it could cause an even larger disaster if you add the wrong amounts of elements together.
You replace the variable by the number, do all specified calculations, and then check whether the resulting inequality is true or false. This is basically not very different from checking a solution of an equation.
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
check the solution.