<s>[INST] addition with a variable (mod) Given $2+x \equiv 7 \pmod 3$.
$2 + 0 = 2$
$2 + 1 = 3$
$2 + 2 = 4$ 
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$2 + 5 = 7$
so, the answer will be $x = 5, 8, 11, 14, 17,\dots$ 
Is this correct? Because somebody told me the answer should be $x = 2, 5, 8, 11, 14, 17,\dots$ 
 [/INST] We are given that:
$(2+x) = 7 (\mod 3)$
Thus, $2+x-7 = 3k$ where $k$ is an integer.
Simplifying, yields:
$x-5 = 3k$
Therefore, $x\in (5,8,..)$
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