Answer:
-4<x<1/3
Step-by-step explanation:
3x²+11x+5<9
3x²+11x-4<0.
First we determine the solutions of
3x²+11x-4=0
Delta=11²-4×3×(-4)=121+48=169=13²
The roots are
x1=(-11-13)/6=-24/6=-4
x2=(-11+13)/6=2/6=1/3
So, we have:
3x²+11x-4=3(x-⅓)(x+4)=(3x-1)(x+4)
So, coming back to our inequality:
(3x-1)(x+4)<0, we note (as we already know) that this condition is satisfied for all those x located between the roots: -4<x<1/3
