Show That for Any Positive Number $\varepsilon$ We Can Find a Positive Number

Multiple Choice

Show that for any positive number $\varepsilon$ we can find a positive number $\delta$ such that the statement below is satisfied.
- $6 \mathrm{x}-7$ is less than $\varepsilon$ away from 5 whenever $\mathrm{x}$ is less than $\delta$ away from 2.

A) $\delta=\frac{\varepsilon}{6}$

B) $\delta=\frac{\varepsilon}{8}$

C) $\delta=\frac{\varepsilon}{4}$

D) $\delta=\frac{\varepsilon}{7}$