Given:
4x – 2 < 8
4x – 2 + 2 < 8 + 2
4x < 10
So divide by 4 on both sides we get,
\( \dfrac{4x}{4} < \dfrac{10}{4}\)
x < \( \dfrac{5}{2}\)
(i) x ∈ R
When x is a real number, the solution of the given inequation is (-∞, \( \dfrac{5}{2}\)).
(ii) x ∈ Z
When, 2 <\( \dfrac{5}{2}\) < 3
So when, when x is an integer, the maximum possible value of x is 2.
The solution of the given inequation is {…, –2, –1, 0, 1, 2}.
(iii) x ∈ N
When, 2 < \( \dfrac{5}{2}\) < 3
So when, when x is a natural number, the maximum possible value of x is 2. We know that the natural numbers start from 1, the solution of the given inequation is {1, 2}.
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