+0

0
209
2
+2709

If $$3x+7\equiv 2\pmod{16}$$ , then $$2x+11$$  is congruent $$\pmod{16}$$ to what integer between 0 and 15 , inclusive?

tertre  Mar 23, 2017
#1
+6979
0

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

MaxWong  Mar 23, 2017
#2
+2709
0

Thanks so much!

tertre  Mar 23, 2017