Solve the given inequation and graph solution on number line :

2y - 3 < y + 1 ≤ 4y + 7, y ∈ R

Given,

2y - 3 < y + 1 ≤ 4y + 7

Solving L.H.S. of the above equation,

⇒ 2y - 3 < y + 1

⇒ 2y - y < 1 + 3

⇒ y < 4 ……..(i)

Solving R.H.S. of the above equation,

⇒ y + 1 ≤ 4y + 7

⇒ 4y- y ≥ 1 - 7

⇒ 3y ≥ -6

⇒ y ≥ -2 …….(ii)

From (i) and (ii) we get,

-2 ≤ y < 4

∴ Solution set = {y : -2 ≤ y < 4, y ∈ R}.

Solution on the number line is :