Question
Given x ∈ {integers}, find the solution set of $:-5 ≤ 2x – 3 < x + 2$
✓
Answer
$-5<=2 x -3< x +2$
$ \Rightarrow-5 \leq 2 x-3 \text { and } 2 x -3< x +2$
$ \Rightarrow-5+3 \leq 2 x \text { and } 2 x-x<2+3 $
$ \Rightarrow-2 \leq 2 x \text { and } x <5$
Since $x \in\{$ integer $\}$
$\therefore$ Solution set $=\{-1,0,1,2,3,4\}$
$ \Rightarrow-5 \leq 2 x-3 \text { and } 2 x -3< x +2$
$ \Rightarrow-5+3 \leq 2 x \text { and } 2 x-x<2+3 $
$ \Rightarrow-2 \leq 2 x \text { and } x <5$
Since $x \in\{$ integer $\}$
$\therefore$ Solution set $=\{-1,0,1,2,3,4\}$
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