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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
`\implies` 2y – 3 – y < y + 1 – y ≤ 4y + 7 – y
`\implies` y – 3 < 1 ≤ 3y + 7
`\implies` y – 3 < 1 and 1 ≤ 3y + 7
`\implies` y < 4 and 3y ≥ –6
`\implies` y ≥ –2
`\implies` –2 ≤ y < 4
The graph of the given equation can be represented on a number line as:
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