Answer
Solution set: $ (-\infty, 0]\cup[4,\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.
$x^{2}-4x \geq 0$
$f(x)=x^{2}-4x \quad $...factor the trinomial...
$f(x)=x(x-4)$
$x(x-4) \geq 0$
2. Solve the equation $f(x)=0$. The real solutions are the boundary points.
$x(x-4)=0$
$x=0$ or $x=4$
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,
$\begin{array}{llll}
Intervals: & (-\infty, 0) & (0,4) & (4,\infty)\\
a=test.val. & -1 & 1 & 5\\
f(a) & (-1)(-5) & (1)(-3) & (5)(1)\\
f(a) \geq 0 ? & T & F & T
\end{array}$
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: $ (-\infty, 0]\cup[4,\infty)$
