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Question
Solve the given inequation and graph the solution on the number line : 2y – 3 < y + 1 ≤ 4y + 7; y ∈ R.
Solution
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
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