Answer
$p\displaystyle \ \ \ >\ \ \ \frac{1}{5}$
Work Step by Step
Applying the properties of inequality, we can
P1. add any number to both sides,
P2. multiply (or divide) both sides with a positive
$\quad $ number to arrive at a valid inequality.
$\quad $ If we
P3. multiply multiply (or divide) both sides with a negative number,
we must change the direction of the inequality sign, to arrive at a valid inequality..
Our goal is to, step by step, isolate the unknown on one side and interpret the result
(which, if any, will be an interval)
-----------------------------
$3p-1<6p+2(p-1)\qquad \qquad $... parenheses
$3p-1<6p+2p-2\qquad $... simplify RHS
$3p-1<8p-2 \qquad \qquad $P1: ...$/-8p$
$-5p-1\ \ \ \frac{1}{5}$
In interval notation:$\qquad (\displaystyle \frac{1}{5}, \infty)$.
