Discussion
If \(|2x - 3| \lt 5, x \in \mathbb{R}\) , then \(x\) lies in the interval
Answer: C
x lies in (-1, 4).
\(|2x - 3| \lt 5\) means the expression lies strictly between -5 and 5.
\[ \begin{aligned} -5 \lt 2x - 3 \lt 5 \\ -2 \lt 2x \lt 8 \\ -1 \lt x \lt 4 \end{aligned} \]
The interval is open because the inequality is strict, which rules out [-1, 4]. (-2, 4) comes from forgetting to halve the lower bound. Check the endpoints: at x = -1 and x = 4 the expression \(|2x - 3|\) equals exactly 5, which the strict inequality excludes.
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