Solve the Linear Congruence $$15 x \equiv 31 ( \bmod 47 ) \text { given that the inverse of } 15 \text { modulo } 47 \text { is } 22 \text {. }$$

Solve the linear congruence $$15 x \equiv 31 ( \bmod 47 ) \text { given that the inverse of } 15 \text { modulo } 47 \text { is } 22 \text {. }$$