Question

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

2y – 3 < y + 1 ≤ 4y + 7, y ∈ R

Answer 1

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: