Solve: -4x > 30, when

(i) x ∈ R

(ii) x ∈ Z

(iii) x ∈ N

Asked by Aaryan | 1 year ago |  56

##### Solution :-

Given:

-4x > 30

So when we divide by 4, we get

$$\dfrac{-4x}{4} > \dfrac{30}{4}$$

-x > $$\dfrac{15}{2}$$

x < $$\dfrac{-15}{2}$$

(i) x ∈ R

When x is a real number, the solution of the given inequation is (-∞,$$\dfrac{-15}{2}$$).

(ii) x ∈ Z

When, -8 < $$\dfrac{-15}{2}$$ < -7

So when, when x is an integer, the maximum possible value of x is -8.

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 ∅.

Answered by Aaryan | 1 year ago

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