List three advantages of p – n junetion diode over diode valve.

The advantages of P – n; junction diode over diode valves are:

(i) It is not bulky

(ii) It does not need time to warm up

(iii) It is cheaper to manufacture in large quantities.

(iv) It needs low voltage to operate.

For what range of values of x is (frac{1}{2})x + (frac{1}{4}) > (frac{1}{3})x + (frac{1}{2})?