Answer
$m>3\\\\$
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)
-----------------------------
$m-(3m-2)+6<7m-19\qquad $
...expand parentheses
$m-3m+2+6<7m-19\qquad $... simplify the LHS
$-2m+8<7m-19 \qquad $P1: ...$/-7m$
$-9m+8\ \ \frac{-27}{-9}$
$m>3$
In interval notation:$\qquad ($3, $\infty)$.
