If $\displaystyle f(x) = 5x - 6$, prove that f is continuous in its domain.

So,

Pick any> 0. Take any sequence{ xn }converging toc. Then there exists an integerNsuch that

| xn - c | < /5

then,

|f(xn)-(5 c - 6)| = |5xn-6-5c+6| = 5|xn-c|<

My question is, why do we have|xn - c | < /5? Why not|xn - c | < ? Where did the 5 come from?

Thanks.