You plug the number back into the original equation. If you have a specific example, that would help.
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Checking your solution in the original equation is always a good idea,simply to determine whether or not you made a mistake.If your solution doesn't make the original equation true, then it's wrong.
11k+7.7=15.4
If you don't learn to solve equations then guess and check is the only way to arrive at new information.
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
There are plenty of places in order for one to learn more about algorithmic equations. However, one might want to check out brief information about algorithmic equations on the website Wikipedia.