Solve the inequation given below. Write the solution set and represent it on the number line:

2y - 3 < y + 1 ≤ 4y + 7, y ∈ R

Given,

⇒ 2y - 3 < y + 1 ≤ 4y + 7

Solving L.H.S. of the inequation,

⇒ 2y - 3 < y + 1

⇒ 2y - y < 1 + 3

⇒ y < 4 ……….(1)

Solving R.H.S. of the inequation,

⇒ y + 1 ≤ 4y + 7

⇒ 4y + 7 ≥ y + 1

⇒ 4y - y ≥ 1 - 7

⇒ 3y ≥ -6

Dividing by 3 on both sides we get,

⇒ y ≥ -2 ………..(2)

From (1) and (2) we get,

⇒ -2 ≤ y < 4

Since, y ∈ R

Hence, solution set = {y : -2 ≤ y < 4, y ∈ R}.

Solution on the number line is :