Question

Solve the given in-equation and graph the solution on the number line.

2y – 3 < y + 1 ≤ 4y + 7, y ∈ R

Answer 1

2y – 3 < y + 1 ≤ 4y + 7, y ∈ R

⟹ 2y – 3 – y < y + 1 – y ≤ 4y + 7 – y

⟹ y – 3 < 1 ≤ 3y + 7

⟹ y – 3 < 1 and 1 ≤ 3y + 7

⟹ y < 4 and 3y ≥ −6 ⇒ y ≥ -2

⟹ -2 ≤ y < 4

The graph of the given equation can be represented on a number line as: