Question

Solve the given inequation 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.
(a) 2y – 3 < y + 1
⇒ 2y – y < 1 + 3
⇒ y < 4
⇒ 4 > y                  ….(i)
(b) y + 1 ≤ 4y + 7
⇒ y – 4y ≤ 7 – 1
⇒ –3y ≤ 6
⇒  3y ≥ 6

⇒ `y ≥ (6)/(-3)`
⇒ y ≥ –2                 ....(ii)
From (i) and (ii),
4 > y ≥ –2 or –2 ≤ y < 4
Now representing it on a number given below