(x^2+3)/(4x)≥1 multiply both sides by 4x
x^2+3≥4x subtract 4x from both sides...
x^2-4x+3≥0 factor left side...
(x-1)(x-3)≥0 for this to be true both terms need to be positive or both terms need to be negative or either one of them are equal to zero.
x≥3 and x≤1 thus the interval is
x=(-oo, 1], [3, +oo)