Answer
$x \lt -\displaystyle \frac{6}{7}$
Work Step by Step
Apply rules from the table "Rules for Inequalities"
$\displaystyle \frac{4}{5}(x-2) \lt \frac{1}{3}(x-6)\quad $ ... multiply with LCD=$15$, (apply rule 3)
$3\cdot 4(x-2) \lt 5(x-6)\quad $ ... distribute
$12x-24 \lt 5x-30 \quad $... add $-5x+24$ (rules 1 and 2)
$ 12x-5x \lt -30+24$
$7x \lt -6\quad $.... multiply with $ c=\displaystyle \frac{1}{7}\quad$ (positive, rule 3)
$x \lt -\displaystyle \frac{6}{7}$
This inequality describes an open interval, $x\displaystyle \in(-\infty,-\frac{6}{7})$
See table "Types of intervals."
