Question
Solve 2 ≤ 2x – 3 ≤ 5, x ∈ R and mark it on number line.
✓
Answer
$
\begin{aligned}
& 2 \leq 2 x-3 \leq 5 \\
& 2 \leq 2 x-3 \text { and } 2 x-3 \leq 5 \\
& 2+3 \leq 2 x \text { and } 2 x \leq 5+3 \\
& 5 \leq 2 x \text { and } 2 x \leq 8 \\
& \therefore \frac{5}{2} \leq x \text { and } x \leq 4 \\
& \therefore \frac{5}{2} \leq x \leq 4 \\
& \therefore \text { Solution set }=\left\{x: x \in R, \frac{5}{2} \leq x \leq 4\right\}
\end{aligned}
$
Solution set on number line
\begin{aligned}
& 2 \leq 2 x-3 \leq 5 \\
& 2 \leq 2 x-3 \text { and } 2 x-3 \leq 5 \\
& 2+3 \leq 2 x \text { and } 2 x \leq 5+3 \\
& 5 \leq 2 x \text { and } 2 x \leq 8 \\
& \therefore \frac{5}{2} \leq x \text { and } x \leq 4 \\
& \therefore \frac{5}{2} \leq x \leq 4 \\
& \therefore \text { Solution set }=\left\{x: x \in R, \frac{5}{2} \leq x \leq 4\right\}
\end{aligned}
$
Solution set on number line
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