A problem regarding congruence

Question

What is(are) the intermediate argument(s) behind the following lines?

\begin{align*} 3t&\equiv 4\mod8\\ \implies t&\equiv4\mod8 \end{align*}

Found it in a number theory text.

Answer 1

$3t \equiv 4\mod 8$

$3t \equiv 4 + 8\mod 8$

$3t\equiv 12\mod 8$

multiplying by the multiplicative inverse of 3 :

$t \equiv 4\mod 8$

It's modulo 8 because $gcd(3,8)=1$ so we keep the modulo 8.

Answer 2

Try multiplying both sides of the equation by $3$. What is the result modulo $8$?