+4622 If \(3x+7\equiv 2\pmod{16}\) , then \(2x+11\) is congruent \(\pmod{16}\) to what integer between 0 and 15 , inclusive?
+9673 If \(3x+7\equiv 2\pmod{16}\), \(3x+5\) is divisible by 16.
The smallest integer solution for x is 9. where 3(9) + 5 = 32 is divisible by 16.
Substitute x = 9, 2x + 11 = 29.
29 mod 16 = 13.
Let's test for the 2nd smallest integer solution for x, which is 25. where 3(25) + 5 = 80 is divisible by 16.
2x + 11 = 61.
61 mod 16 = 13.
Good!!
Therefore, the answer is 13 :D
