Solve the given inequation and graph the solution on the number line
$2 y - 3 < y + 1 \leq 4 y + 7; y ϵ R$

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Solution

$G i v e n : 2 y - 3 < y + 1 \leq 4 y + 7; y ϵ R$
$\Rightarrow 2 y - y < 3 + 1; 1 - 7 \leq 4 y - y$
$\Rightarrow y < 4;$ $- 6 \leq 3 y$
$\Rightarrow y < 4;$ $- 2 \leq y$
Hence, the solution set $= {- 2 \leq y < 4, y ϵ R}$
The graph of the solution is shown below.

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