Question

Can anyone help me solve this problem below:
3x2−5x−2
___________ <0
x2−9

Answer 1

`-(1)/(3) < x < 2` and -3 < x < 3

Explanation:

The inequality equation is

3x² - 5x - 2 < 0

⇒ 3x² - 6x + x - 2 < 0

⇒ (x - 2)(3x + 1) < 0

Therefore, either (x - 2) > 0 and (3x + 1) < 0

⇒ x > 2 and
`x < -(1)/(3)` which is not possible for any particular value of x.

or, (x - 2) < 0 and (3x + 1) > 0

⇒ x < 2 and
`x > -(1)/(3)` which is valid.

So, the solution is
`-(1)/(3) < x < 2` (Answer)

Now, another inequality is

x² - 9 < 0

⇒ x² < 9

Therefore, -3 < x < 3 is the solution. (Answer)