"Plug in" the two limits of your answer to check the interval. They do NOT match the problem criteria.
The final answer will be in the form you provided, but the values on the upper and lower limits must match those of the problem (0 and 1/2).
Substituting your values into the inequality:
(2(2)+4)^-1 = 1/8
(2(1)+4)^-1 = 1/6 do not span the inequality given.
You must solve it for the limits:
(2(x1)+4)^-1 = 0
(2(x2)+4)^-1 = 1/2
THEN you will have the range BETWEEN which the 'x' must be to satisfy the inequality. x1 < x < x2