Find the value of x, which satisfy the inequation - 2*5/6 less than1/2 -2x/3 less than aur equal to 2 and x€W and represent the solution on the numbe line.[icse 10th 2014]

Find the value of x, which satisfy the inequation and x ∈ W and represent the solution on the number line. 

Given that - 2 *5/6 < 1/2 - (2x)/3 ≤ 2 

=>  - 17/6 < 1/2 - (2x)/3 ≤ 2 

=> - 17/6 < 1/2 - (2x)/3 and 1/2 - (2x)/3≤ 2 

Case I  - 17/6 < 1/2 - (2x)/3

Multiplying both sides by 6, we get, 

- 17 < 3 - 4x

Subtracting both sides by 3, we get,

- 17 - 3 < 3 - 4x - 3

- 20 < - 4x

Dividing both sides by -4, we get,

5>x

or x < 5  -  - - - - - (1) 

[It both sides of  an inequality is divided by the same negative number,then sign of inequality reverses.]

Case 2:- 1/2 -2x/3 ≤ 2 

Subtracting both sides  1/2 we get,

=> 1/2 - (2x)/3 - 1/2 ≤ 2 - 1/2

=>  - (2x)/3 ≤ 3/2

Multiplying both sides by 3, we get

- 2x ≤ 9/2

Dividing both sides by -2, we get,

x ≥ - 9 /4   =>  - 9/4 ≤ x   - - - - - - - - (2)

From (1) and (2), we get,

- 9/4 ≤ x < 5

=> x=[ -9/4, 5)

But x is a whole Numbers, i.e  {W=0, 1, 2, 3, 4, 5, ...}

So the solution set ={x ; x = 0, 1, 2, 3, 4}