Question

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

Answer 1

C

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

Answer 2

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