Discussion
If \(10 \lt |x + 10| \leq 25\) , then \(x\) lies in
Answer: C
\(x\) lies in \([-35, -20) \cup (0, 15]\).
\(10 \lt |x + 10| \leq 25\) means \(x + 10\) is more than 10 but at most 25 away from 0, on either side:
\[ \begin{aligned} 10 \lt x + 10 \leq 25 &\Rightarrow 0 \lt x \leq 15 \\ -25 \leq x + 10 \lt -10 &\Rightarrow -35 \leq x \lt -20 \end{aligned} \]
The strict inequality at 10 makes 0 and -20 excluded (round brackets), and the non-strict one at 25 makes 15 and -35 included (square brackets). The other options have a wrong endpoint.
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