How close to -4 do we have to take x so that

Question

1/(x+4)³ > 10,000

Answer 1

If

1/(x+4)^3 > 10,000

then

1/10,000> (x+4)^3

cube root of (1/10,000) > x+4

Therefore, the distance between x and -4 which is

x - (-4) = x+4

should be smaller than

cube root of (1/10,000) = 0.046