Solve the following inequality and write down the solution set :

11x - 4 < 15x + 4 ≤ 13x + 14, x ∈ W

Represent the solution set on a real number line.

Given,

⇒ 11x - 4 < 15x + 4 ≤ 13x + 14

Solving L.H.S. of the inequation,

⇒ 11x - 4 < 15x + 4

⇒ 15x + 4 > 11x - 4

⇒ 15x - 11x > -4 - 4

⇒ 4x > -8

⇒ x > $-\dfrac{8}{4}$

⇒ x > -2 ……….(1)

Solving R.H.S. of the inequation,

⇒ 15x + 4 ≤ 13x + 14

⇒ 15x - 13x ≤ 14 - 4

⇒ 2x ≤ 10

⇒ x ≤ $\dfrac{10}{2}$

⇒ x ≤ 5 …….(2)

From (1) and (2) we get,

-2 < x ≤ 5

Since, x ∈ W

Hence, solution set = {0, 1, 2, 3, 4, 5}.

Solution on the number line is :