Answer
Solution set: the empty set, $\emptyset$.
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.
$f(x)=x^{2}-6x+9<0$
factor the trinomial...
find factors of $9$ that add to $-6:$
$f(x)=(x-3)(x-3)<0$
2. Solve the equation $f(x)=0$. The real solutions are the boundary points.
$(x-3)(x-3)=0$
$x=3$
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,
$\begin{array}{llll}
Intervals: & (-\infty, -3) & (-3,\infty) & \\
a=test.val. & -10 & 0 & \\
f(a) & (-13)(-13) & (3)(3) & \\
f(a) < 0 ? & F & F &
\end{array}$
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.
No intervals satisfy the inequality, border 3 is excluded...
Solution set: the empty set, $\emptyset$.
