Solve the following linear inequations in R

4x – 2 < 8, when

i. x ∈ R

ii. x ∈ Z

iii. x ∈ N

Given 4x – 2 < 8

⇒ 4x – 2 + 2 < 8 + 2

⇒ 4x < 10

i. x ∈ R

When x is a real number, the solution of the given inequation is.

ii. x ∈ Z

As, 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, 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}.

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