Answer
Set notation:$\quad \{x|3\leq x \leq 5\}$.
Interval notation: $\quad[3,5]$.
The graph is shown below.
Work Step by Step
Separate into two inequalities.
$0\leq 2x-6\quad$ and $\quad 2x-6 \leq 4 $
Add $6$ to both sides of each inequality.
$0+6\leq 2x-6+6 \quad $ and $\quad 2x-6+6 \leq 4+6 $
Simplify.
$6\leq 2x \quad$ and $\quad2x\leq 10 $
Divide both sides by $2$.
$\dfrac{6}{2}\leq \dfrac{2x}{2} \quad$ and $\quad\dfrac{2x}{2}\leq \dfrac{10}{2} $
Simplify.
$3 \leq x $ and $x \leq 5 $
The solution set is $\{x|3\leq x \leq 5\}$.
or interval notation is $[3,5]$.
To graph, use an open bracket at $3$ and a close bracket at $5$ and shade the region in between.
