Answer
Set notation:$\quad \{x|1\leq x \leq 4\}$
Interval notation:$\quad [1,4]$.
The graph is shown below.
Work Step by Step
Separate into two inequalities.
$4\leq 2x+2 \quad $ and $\quad 2x+2 \leq 10 $
Subtract $2$ to both sides of each inequality.
$4-2\leq 2x+2 -2\quad $ and $\quad2x+2-2 \leq 10 -2$
Simplify.
$2\leq 2x\quad $ and $\quad2x \leq 8$
Divide both sides by $2$.
$\dfrac{2}{2}\leq \dfrac{2x}{2} \quad $ and $\quad \dfrac{2x}{2}\leq \dfrac{8}{2} $
Simplify.
$1 \leq x \quad$ and $\quad x \leq 4 $
The solution set is $\{x|1\leq x \leq 4\}$.
or interval notation is $[1,4]$.
To graph, use an open bracket at $1$ and a close bracket at $4$ and shade the region in between.
