Solve the following linear equations:
$\frac{1}{3}(7x-1)=\frac{1}{4}$

Solving the equation for $x$,

$\frac{1}{3}(7x-1)=\frac{1}{4}\Rightarrow \frac{7x-1}{3}=\frac{1}{4}$

By cross multiplication,

$\Rightarrow 4(7x-1)=3\times 1\Rightarrow 28x-4=3\Rightarrow 28x=3+4\Rightarrow 28x=7\Rightarrow x=\frac{7}{28}=\frac{1}{4}$

Hence, $x=\frac{1}{4}$