Answer
Solution set: $[1,2]\cup[3,\infty)$
Work Step by Step
Follow the "Procedure for Solving Polynomial lnequalities",\ p.412:
1. Express the inequality in the form $f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$
where $f$ is a polynomial function.
$(x-1)(x-2)(x-3)\geq 0$
$f(x)=(x-1)(x-2)(x-3)$
2. Solve the equation $f(x)=0$. The real solutions are the boundary points.
$(x-1)(x-2)(x-3)=0$
$x=1$ or $x=2$ or $x=3$
3. Locate these boundary points on a number line, thereby dividing the number line into intervals.
4. Test each interval's sign of $f(x)$ with a test value,
$\begin{array}{llll}
Intervals: & a=test.v. & f(a),signs & f(a) \geq 0 ? \\
(-\infty,1) & 0 & (-)(-)(-) & F\\
(1,2) & 1.5 & (+)(-)(-) & T\\
(2,3) & 2.5 & (+)(+)(-) & F\\
(3,\infty) & 5 & (+)(+)(+) & T
\end{array}$
5. Write the solution set, selecting the interval or intervals that satisfy the given inequality. If the inequality involves $\leq$ or $\geq$, include the boundary points.
Solution set: $[1,2]\cup[3,\infty)$