6. Given a five-digit number. If you prepend a seven to the number, the resulting six-digit number will be 5 times larger than the six-digit number obtained by appending a seven to the end. Find this five-digit number.
6. Solution. Let \(x\) be a five-digit number. If we prepend a seven to it, we get the number \(7 \cdot 10^{5} + x\). If we append a seven to it, we get the number \(10 x + 7\). According to the problem,

\[
7 \cdot 10^{5} + x = 5(10 x + 7)
\]

Solving this equation, we get \(x = 14285\).