To solve the inequality 4x > 1, we divide both sides by 4:

4x > 1
x > 1/4

Now, let's solve the second inequality:

5 - 2x > 2

Subtract 5 from both sides:

-2x > 2 - 5
-2x > -3

Divide by -2 (note that dividing by a negative number switches the inequality sign):

x < 3/2

Therefore, the solution to the system of inequalities is x > 1/4 and x < 3/2.