Solve: 4x-2 < 8, when

(i) x ∈ R

(ii) x ∈ Z

(iii) x ∈ N

Asked by Aaryan | 1 year ago |  62

##### Solution :-

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}.

Answered by Aaryan | 1 year ago

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