Answer
$(-\infty,-2]\cup[4,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | \frac{3x-3}{9}\right |\geq1$
Rewrite the inequality without absolute value bars.
$\Rightarrow \frac{3x-3}{9}\leq-1$ or $\frac{3x-3}{9}\geq1$
Solve each inequality separately.
Multiply all parts by $9$.
$\Rightarrow \frac{3x-3}{9}(9)\leq-1(9)$ or $\frac{3x-3}{9}(9)\geq1(9)$
Simplify.
$\Rightarrow 3x-3\leq-9$ or $3x-3\geq9$
Add $3$ to all parts.
$\Rightarrow 3x-3+3\leq-9+3$ or $3x-3+3\geq9+3$
Simplify
$\Rightarrow 3x\leq-6$ or $3x\geq12$
Divide all parts by $3$.
$\Rightarrow \frac{3x}{3}\leq\frac{-6}{3}$ or $\frac{3x}{3}\geq\frac{12}{3}$
Simplify.
$\Rightarrow x\leq-2$ or $x\geq4$
The solution set is less than or equal to $-2$ or greater than or equal to $4$.
The interval notation is
$(-\infty,-2]\cup[4,\infty)$.
