Ben said the graph of the inequality - x ^(2) + 9 > 0 shows the solution is x < -3 or x > 3. Is Ben correct? Explain.​

Question

Ben said the graph of the inequality


`- x ^(2) + 9 > 0`
shows
the solution is x < -3 or x > 3. Is Ben correct? Explain.​

Answer 1

Ben is incorrect

The solutions are x>-3 and x < 3

Explanation:

we have

`-x^(2) +9 > 0`

Multiply by -1 both sides

`x^(2) -9 < 0`

Adds 9 both sides

`x^(2) < 9`

The solutions are

`x < 3`

and

`-x < 3` -----> Multiply by -1 both sides ---->
`x > -3`

therefore

The solution is the interval (-3,3)

Ben is incorrect