find a solution of 9x = 24 (mod 21) I need help finding a solution of $9x\equiv {24}\pmod {21}$.
Here is what I tried, but it's wrong.
mod x is the positive value of x. mod $21 = 21.$
$9x\equiv {24}\pmod {21}$.
$9x = 24*21$
$x = 24*21/9 = 56$

$$9x=24\pmod{21}\iff 9x=24+21k=3+21m\;,\;k\,,\,m\in\Bbb Z\implies$$
$$3x=1+7k\implies x=5\pmod 7$$
since $\,3\cdot 5=15=1\pmod 7\iff 3^{-1}=5\pmod 7\;$
