Question

(a) Solve the given inequality 3 (x +2) ≥ 5 (x + 1).

(b) Find the greatest possible value of x, if it is;
1. a rational number
2. an integer
3. a prime number

Answer 1

3x + 6 >= 5x + 5
3x - 5x >= 5 - 6
-2x >= -1
x <= -1/-2 = 0.5

If x is rational then greatest x = 1/2
If x is an integer then greatest x = 0
If x is prime then there is no valid value of x