Multiply through by 4x: 1-8x>0, 1>8x or 8x<1; divide through by 8: x<1/8.
Check: put in a value of x that obeys this inequality. For example, x=1/10. Work out 1/4x=1/(4/10)=10/4=5/2, so the original inequality becomes 5/2-2 which equals 1/2, which is greater than zero. Now use a value of x that disobeys the inequality x<1/8. Put x=1/2. The original inequality now becomes 1/2-2 which is less than zero and disobeys the inequality. Finally put x=1/8: the inequality becomes 2-2 which is zero, and therefore not greater than 0. So at the borderline the value 1/8 disobeys x<1/8 and 1/(4x)-2<0.