keeping in mind that, an absolute value, is in effect a piece-wise function, so is a duplet, so |whatever here| is really two siblings, the positive and negative siblings +(whatever here) and -(whatever here), thus
[tex]\bf \cfrac{|3v-1|}{5}\ge 4\implies |3v-1|\ge 20\implies
\begin{cases}
+(3v-1)\ge 20\\
-(3v-1)\ge 20
\end{cases}\\\\
-------------------------------\\\\
+(3v-1)\ge 20\implies 3v-1\ge 20\implies 3v\ge 21\implies v\ge \cfrac{21}{3}
\\\\\\
\boxed{v\ge 7}\\\\
-------------------------------\\\\[/tex]
[tex]\bf -(3v-1)\ge 20\implies -3v+1\ge 20\implies -3v\ge 19
\\\\\\
\stackrel{\textit{negative division, the sign changes}}{v\le \cfrac{19}{-3}}\implies \boxed{v\le -\cfrac{19}{3}}\\\\
-------------------------------\\\\
7\le v\le -\cfrac{19}{3}[/tex]
