Question

What are the solutions to the inequality (x-3)(x+5) greater than or equal to 0?

Answer 1

For this case we must find the solutions of the following inequality:

$(x-3)(x+5)\leq0$

For $(x-3)(x+5)=0$we have the following solutions:

$x=3\\x=-5$

As a possible solution we have the following intervals:

$x\leq -5\\-5\leq x\leq 3\\x\geq 3$

We must choose a value included in each of the possible intervals, replace them in the original inequality and verify if it is fulfilled.

• $x\leq -5$

$(-6-3)(-6+5)\leq 0\\-9*-1\leq0\\ 9\leq0$

It is not true

• $-5\leq x\leq 3$

$(0-3)(0+5)\leq 0\\-3*5\leq 0\\-15\leq0$

It is true.

ANswer:

Option C

Answer 2

Answer:

C

Step-by-step explanation:

If this was an equation...

(x-3)(x+5) = 0

x = 3, -5

So 3 and -5 are the minimum and the maximums.

So we convert that into an inequality.

-5 <= x <= 3