Solve the given inequation and graph the solution on the number line.

$2 y - 3 < y + 1 \leq 4 y + 7, y \in R$

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Solution

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:

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Solve the following inequation and graph the solution on number line,

2y – 3 < y + 1 < 4y + 7: y ε R.

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