Solve the following inequation and graph the solution set on the number line:
$2 x - 3 < x + 2 \leq 3 x + 5, x ϵ R$
[3 MARKS]

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Solution

Solving each inequation: 1 Mark each
Solution on number line: 1 Mark

$G i v e n : 2 x - 3 < x + 2 \leq 3 x + 5, x ϵ R$
First, we take 2x - 3 < x + 2
$\Rightarrow 2 x - x < 2 + 3$
[Transposing the terms]
$\Rightarrow x < 5$ ...(i)
Now, $x + 2 \leq 3 x + 5$
$\Rightarrow 2 - 5 \leq 3 x - x$
$\Rightarrow - 3 \leq 2 x$
$\Rightarrow - 1.5 \leq x$ ...(ii)
From equations (i) and (ii), we get $- 1.5 \leq x < 5$
$∴$ Solution set is ${x : - 1.5 \leq x < 5, x ϵ R}$
Graph of the solution set is as follows:

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