Solve the following inequation and graph the solution set on the number line :

$2 x - 3 < x + 2 \leq 3 x + 5; x \in R .$

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Solution

2x – 3 < x + 2 ≤ 3x + 5
2x – 3 < x + 2 and x + 2 ≤ 3x + 5
x < 5 and -3 ≤ 2x
x < 5 and -1.5 ≤ x
Solution set = {-1.5 ≤ x < 5}
The solution set can be graphed on the number line as:

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