Answer
$x\displaystyle \leq-\frac{1}{3}$
Work Step by Step
Apply rules from the table "Rules for Inequalities"
$2x-\displaystyle \frac{1}{2}\geq 7x+\frac{7}{6}\quad $ ... multiply with LCD=6, (apply rule 3)
$12x-3\geq 42x+7\quad $... add $-12x-7$ (rules 1 and 2)
$-3-7\geq 42x-12x$
$-10\geq 30x\quad $.... multiply with $ c=\displaystyle \frac{1}{30}\quad$ (positive, rule 3)
$-\displaystyle \frac{1}{3}\geq x$
$x\displaystyle \leq-\frac{1}{3}$
This inequality describes a closed interval, $x\displaystyle \in(-\infty,-\frac{1}{3}]$
See table "Types of intervals."
