What is the least positive $x$ with $5x \equiv 3 \pmod{8}$?

Explanation

1. 01

   The inverse of 5 modulo 8 is 5, since $5 \times 5 = 25 \equiv 1$.

2. 02

   Multiply both sides by 5: $x \equiv 15 \equiv 7$. Check: $5 \times 7 = 35 = 32 + 3$.