Question
If x ∈ Z, solve 2 + 4x < 2x – 5 ≤ 3x. Also represent its solution on the number line.
✓
Answer
$ \begin{aligned} & 2+4 x<2 x-5 \leq 3 x \\ & 2+4 x<2 x-5 \text { and } 2 x-5 \leq 3 x=>4 x-2 x<-5-2 \text {, and } 2 x-3 x \leq 5 \\ & \Rightarrow 2 x<-7 \text { and }-x \leq 5 \\ & \Rightarrow x<-\frac{7}{2} \text { and } x \geq-5 \text { and }-5 \leq x \\ & \therefore-5 \leq x<-\frac{7}{2} \\ & \because x \in Z \end{aligned} $
$\therefore$ Solution set $=\{-5,-4\}$
Solution set on Number line
$\therefore$ Solution set $=\{-5,-4\}$
Solution set on Number line
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