Solve the following inequation and write down the solution set. 11x-4 < 15x+4 <= 13x+14 ; xεW. Represent the solution on a number line. [icse 2019]

Question: Solve the following inequation and write down the solution set.

11x - 4 < 15x + 4 ≤ 13x + 14 ; x εW

Represent the solution on the number line.

Given that:

11x - 4 < 15x + 4 ≤13x + 14 - - - - - - - (1)

=> 11x - 4 < 15x + 4 and 15x + 4 ≤13x + 14

Case I.

11x - 4 < 15x + 4

Subtracting 11x on both sides, we get,

-4 < 4x +4

Subtracting '4' on both sides, we get,

-8 < 4x

Dividing both sides by 4, we get,

-2 < x 

or x > -2. - - - - - - (2)

Case II.

15x + 4 ≤ 13x + 14

Subtracting both sides by 13x, we get,

2x + 4 ≤ 14

Subtracting 4 on both sides, we get,

2x  ≤10

Dividing both sides by 2, we get

x ≤ 5 - - - - - - - (3)

From,(1), (2) and (3), the solution set is

- 2 < x ≤ 5 :xεW

=(-2,5], here W is a whole number.

W = 0, 1, 2, 3 ,- - - - - - - - .

So the solution set will be {0,1,2,3,4,5}