What does $a\equiv b\pmod n$ mean? What does the $\equiv$ and $b\pmod n$ mean?
for example, what does the following equation mean?
$5x \equiv 7\pmod {24}$? Tomorrow I have a final exam so I really have to know what is it.

It’s a bit late to be learning a basic definition, but here it is: $a\equiv b\pmod n$ means that $n\mid a-b$, i.e., that $a-b$ is a multiple of $n$. Thus, the congruence $5x\equiv 7\pmod{24}$ means that $24\mid 5x-7$. To solve it, you must find an integer $x$ that makes this true. Since $5\cdot11-7=55-7=48$ is a multiple of $24$, $x\equiv 11\pmod{24}$ is a solution.
