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The best way is to learn is to look at examples, and see how they work.
One of the simplest "real" context-free languages is $\{\; a^mb^n \mid n = m \;\}$
Its grammar is $S\to aSb\mid \varepsilon$.
Now add in steps, the extra 3, and the more than ...
$\{\; a^mb^n \mid n = m+3 \;\}$
$\{\; a^mb^n \mid n \le m+3 \;\}$
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The unequal number of $a$'s and $b$'s have
{equal number of $a$'s and $b$'s} with {{extra $a$'s } or {extra $b$'s}}
Extra $a$'s or extra $b$'s can be
at the beginning
at the end
in between (ANY WHERE) and any number of times
Let $P$ derive strings with extra $a$'s
Let $Q$ derive strings with extra $b$'s
Let $X$ derive equal number of $a$'s and $b$'s
Let $A$...
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