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If 3x+7=2+x+5 (mod 16), then 2x+11+x+3 is congruent (mod 16) to what integer between 0 and 15, inclusive?

 Jan 8, 2022
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\(3x+7\equiv 2+x+5\;\;mod 16)\\ 2x\equiv 0 (mod 16)\\ x\equiv 8N\\ ~\\ 2x+11+x+3\;\; (mod16) \\ \equiv 0+x+14\;\; (mod16) \\ \equiv 8N-2 \;\; (mod16) \\ \)


So I think  \(2x+11+x+3(mod 16) \equiv 6\;(mod 16) \quad or \quad 14\;(mod 16) \)

 

 

I am not 100% certain that this is correct.     Please give feedback.

 

 

 

LaTex

3x+7\equiv  2+x+5\;\;mod 16)\\
2x\equiv  0 (mod 16)\\
x\equiv  8N\\
~\\
2x+11+x+3\;\; (mod16) \\
\equiv  0+x+14\;\; (mod16) \\
\equiv  8N-2 \;\; (mod16) \\

 Jan 8, 2022

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