Given as
4x – 2 < 8
4x – 2 + 2 < 8 + 2
4x < 10
Therefore divide by 4 on both sides we get,
4x/4 < 10/4
x < 5/2
(i) Given as x ∈ R
When x is a real number, the solution of the given inequation is (-∞, 5/2).
(ii) Given as x ∈ Z
When, 2 < 5/2 < 3
Therefore 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) Given as x ∈ N
When, 2 < 5/2 < 3
Therefore when, when x is a natural number, the maximum possible value of x is 2. As we know that the natural numbers start from 1, the solution of the given inequation is {1, 2}.
