For this case we must find the solutions of the following inequality:
[tex](x-3)(x+5)\leq0[/tex]
For [tex](x-3)(x+5)=0[/tex]we have the following solutions:
[tex]x=3\\x=-5[/tex]
As a possible solution we have the following intervals:
[tex]x\leq -5\\-5\leq x\leq 3\\x\geq 3[/tex]
We must choose a value included in each of the possible intervals, replace them in the original inequality and verify if it is fulfilled.
[tex](-6-3)(-6+5)\leq 0\\-9*-1\leq0\\ 9\leq0[/tex]
It is not true
- [tex]-5\leq x\leq 3[/tex]
[tex](0-3)(0+5)\leq 0\\-3*5\leq 0\\-15\leq0[/tex]
It is true.
ANswer:
Option C
