The value of \( m \) satisfying \( m\equiv 12\pmod 7 \) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −9
\( m\equiv 12\pmod 7 \) means 7 divides m − 12. For each option:
\( \displaystyle m=3:\ 3-12=-9,\ \text{not divisible by 7} \)
\( \displaystyle m=-3:\ -3-12=-15,\ \text{not divisible by 7} \)
\( \displaystyle m=9:\ 9-12=-3,\ \text{not divisible by 7} \)
\( \displaystyle m=-9:\ -9-12=-21=7\times(-3) \)
So m = −9.