Question

Solve: 12 x > 30, when

1. x is a natural number
2. x is an integer

Answer 1

The given inequality is:

–12x > 30

⇒ $-\frac {12x}{-12} < \frac {30}{-12 }$ [Dividing both sides by same negative number ]

⇒ $x< -\frac {5}{2}$

---

(i) There is no natural number less than $(-\frac {5}{2})$.
Thus, when x is a natural number, there is no solution of the given inequality.

---

(ii) The integers less than $(-\frac {5}{2})$ are …, –5, –4, –3.
Thus, when x is an integer, the solutions of the given inequality are …, –5, –4, –3.
Hence, in this case, the solution set is {…, –5, –4, –3}.