Question

Solve for x. Answer in Interval Notation using Grouping Symbols.
x^2+9x<-20

Answer 1

-5 < x <-4 is the answer.

Explanation:

We have an inequality:

x²+9x<-20

We have to solve it for x.

Adding 20 on both sides of inequality we get,

x²+9x+20< -20+20

x²+9x+20 < 0

Now, we have to find two numbers whose sum is 9 and whose product is 12.

that are 4 and 5 then we use factorization to solve it we get,

(x+5)(x+4)<0

either (x+5) < 0 or (x+4) < 0

therefore the the values of x lie in the following interval:

-5< x <-4 is the answer.

Answer 2

In interval notation:

(-5,-4)

Explanation:

To solve the expression shown in the problem you must:

- Add 20 to both sides, then:

`x^(2)+9x+20<-20+20\\x^(2)+9x+20<0`

- Now you must find two number whose sum is 9 and whose produt is 20. These would be 4 and 5. Then, you have:

`(x+4)(x+5)<0`

- Therefore the result is:

`-5<x<-4`

In interval notation:

(-5,-4)