Math Problem Solver

There is no solution for $x$ in the congruence relation $2 x + 2 \equiv 3 \pmod{4}$.

Collect like terms, with constants on one side, and variables on the other: $2 x \equiv 1 \pmod{4}$.

For a linear congruence of the form $a x \equiv b \pmod{n}$, there are zero solutions for $x$ if $\operatorname{gcd}\left(a,n\right)$ does not divide $b$.
$\operatorname{gcd}\left(2, 4\right) = 2$, which does not divide $1$.
Therefore, no value of $x$ is a solution for $2 x \equiv 1 \pmod{4}$.