Answer
N = 15
Work Step by Step
We can graph the function $f(x) = \frac{3x^2+1}{2x^2+x+1}$
On the graph , we can see that $~~1.45 \lt f(x) \lt 1.5~~$ when $~~x \gt 15$
Therefore:
If $x \gt 15,~~~$ then $~~~\vert \frac{3x^2+1}{2x^2+x+1} - 1.5 \vert \lt 0.05$
We can check the value $N=15$ in the function:
$f(15) = \frac{3(15)^2+1}{2(15)^2+(15)+1} = 1.4506$
