x^3+10x^2+31x <= -30

Question

(2x/x+1) <= (4/x-3)

if the signs mess up there both less than or equal too.

Answer 1

for large negative x the left gets very large negative

for x = 0, the left is 0 and for any positive x the left is +

so the question is when does it get below 30

-1 -> -1 +10 -31 = -22
-2 -> -8 +40 -62 = -30 right there at x = -2