Given,
4x – 2 < 8
⇒ 4x – 2 + 2 < 8 + 2
⇒ 4x < 10
⇒ \(\frac{4x}{4}\) < \(\frac{10}{4}\)
∴ x < \(\frac{5}{2}\)
i. x ∈ R
When x is a real number, the solution of the given inequation is (-∞,\(\frac{5}{2}\)).
ii. x ∈ Z
As 2<\(\frac{5}{2}\)<3,
When x is an integer,
The maximum possible value of x is 2.
Thus,
The solution of the given inequation is {…, –2, –1, 0, 1, 2}.
iii. x ∈ N
As 2<\(\frac{5}{2}\)<3,
When x is a natural number, the maximum possible value of x is 2 and we know the natural numbers start from 1.
Thus,
The solution of the given inequation is {1, 2}.
