Given,
12x < 50
⇒ \(\frac{12x}{12}\) < \(\frac{50}{12}\)
∴ x < \(\frac{25}{6}\)
i. x ∈ R
When x is a real number, the solution of the given inequation is (-∞,\(\frac{25}{6}\)).
ii. x ∈ Z
As 4 < \(\frac{25}{6}\) < 5,
When x is an integer, the maximum possible value of x is 4.
Thus,
The solution of the given inequation is {…, –2, –1, 0, 1, 2, 3, 4}.
iii. x ∈ N
As 4 < \(\frac{25}{6}\) < 5,
When x is a natural number, the maximum possible value of x is 4 and we know the natural numbers start from 1.
Thus,
The solution of the given inequation is {1, 2, 3, 4}.
