Question

Solve the congruence 2x 3 (mod 11):

Answer 1

$2x\equiv3\pmod{11}$

Since 3 * 4 = 12 = 1 mod 11, we can multiply both sides by 4 to get

$4\cdot2x\equiv3\cdot4\pmod{11}\implies8x\equiv1\pmod{11}$

Since 8 * 7 = 56 = 1 mod 11, multiplying both sides by 7 gives

$7\cdot8x\equiv7\cdot1\pmod{11}\implies x\equiv7\pmod{11}$