Answer
Solution set: $ (-\infty, -3)\cup(5,\infty)$
Work Step by Step
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.
$f(x)=(x+3)(x-5)>0$
2. Solve the equation $f(x)=0$. The real solutions are the boundary points.
$(x+3)(x-5)=0$
$x=-3$ or $x=5$
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,
$\left[\begin{array}{llll}
Intervals: & (-\infty, -3) & (-3,5) & (5,\infty)\\
a=test.value & -10 & 0 & 10\\
f(a) & (-7)(-15) & (3)(-5) & (13)(5)\\
f(a) > 0 ? & T & F & T
\end{array}\right]$
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, -3)\cup(5,\infty)$
