Answer
$(-\infty,-2]\cup[7,\infty)$.
Work Step by Step
The given inequality is an absolute value inequality in the form $|a|\geq c$ which can be written without absolute value bars as
$a\leq -b$ or $a\geq b.$
Rewrite the fiven inequality.
$\Rightarrow 2x-5\leq-9$ or $2x-5\geq9$
Add $5$ to all parts.
$\Rightarrow 2x-5+5\leq-9+5$ or $2x-5+5\geq9+5$
Simplify.
$\Rightarrow 2x\leq-4$ or $2x\geq14$
Divide all parts by $2$.
$\Rightarrow \frac{2x}{2}\leq\frac{-4}{2}$ or $\frac{2x}{2}\geq\frac{14}{2}$
Simplify.
$\Rightarrow x\leq-2$ or $x\geq7$
The solution set is the set of real numbers less than or equal to $-2$ or greater than or equal to $7$.
The interval notation is
$(-\infty,-2]\cup[7,\infty)$.
We used square brackets because $-2$ and $7$ belong to the solution set.
