Answer:
[tex]-\frac{1}{3} < x < 2[/tex] and -3 < x < 3
Step-by-step 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 [tex]x < -\frac{1}{3}[/tex] which is not possible for any particular value of x.
or, (x - 2) < 0 and (3x + 1) > 0
⇒ x < 2 and [tex]x > -\frac{1}{3}[/tex] which is valid.
So, the solution is [tex]-\frac{1}{3} < x < 2[/tex] (Answer)
Now, another inequality is
x² - 9 < 0
⇒ x² < 9
Therefore, -3 < x < 3 is the solution. (Answer)
