Given,
–4x > 30
⇒ \(-\frac{4x}{4}\) > \(\frac{30}{4}\)
⇒ - x > \(\frac{15}{2}\)
∴ x < \(-\frac{15}{2}\)
i. x ∈ R
When x is a real number, the solution of the given inequation is (-∞,\(-\frac{15}{2}\)).
ii. x ∈ Z
As - 8 < \(-\frac{15}{2}\) < -7,
When x is an integer, the maximum possible value of x is –8.
Thus,
The solution of the given inequation is {…, –11, –10, –9, –8}.
iii. x ∈ N
As natural numbers start from 1 and can never be negative, when x is a natural number, the solution of the given inequation is ∅.
