Solve: 12x < 50, when

(i) x ∈ R

(ii) x ∈ Z

(iii) x ∈ N

Asked by Aaryan | 1 year ago |  58

##### Solution :-

Given:

12x < 50

So when we divide by 12, we get

$$\dfrac{ 12x}{ 12} < \dfrac{50}{12}$$

x <$$\dfrac{25}{6}$$

(i) x ∈ R

When x is a real number, the solution of the given inequation is (-∞, $$\dfrac{25}{6}$$).

(ii) x ∈ Z

When, 4 <$$\dfrac{25}{6}$$ < 5

So when, when x is an integer, the maximum possible value of x is 4.

The solution of the given inequation is {…, –2, –1, 0, 1, 2, 3, 4}.

(iii) x ∈ N

When, 4 < $$\dfrac{25}{6}$$ < 5

So when, when x is a natural number, the maximum possible value of x is 4. We know that the natural numbers start from 1, the solution of the given inequation is {1, 2, 3, 4}.

Answered by Aaryan | 1 year ago

### Related Questions

#### Solve each of the following in equations and represent the solution set on the number line

Solve each of the following in equations and represent the solution set on the number line $$\dfrac{5x}{4}-\dfrac{4x-1}{3}>1,$$ where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line.

Solve each of the following in equations and represent the solution set on the number line.$$\dfrac{5x-8}{3}\geq \dfrac{4x-7}{2}$$, where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9,

Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9, where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6

Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6, where x ϵ R.