Solve the following inequation and represent the solution set on the number line:
$2 y - 3 \leq y + 1 \leq 4 y + 7, y ϵ R .$

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Solution

$2 y - 3 \leq y + 1 \leq (4 y + 7), y ϵ R \Rightarrow 2 y - 3 - 1 \leq y \leq 4 y + 7 - 1 \Rightarrow 2 y - 4 \leq y \leq 4 y + 6 \Rightarrow 2 y - 4 \leq y a n d y \leq 4 y + 6 \Rightarrow y \leq 4 a n d - 6 \leq 3 y \Rightarrow - 2 \leq y \leq 4$
$∴$ Solution set on the number line is:

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