Mathematics

Mathematics

Problem

A quality check requires the length LL (in cm) of a metal rod to satisfy 15≤2.5L−2<3015 \le 2.5L - 2 < 30. (i) Determine the range of permissible values of LL. (ii) List all integer lengths that meet this requirement.
Intuitive explanation

This problem is about solving compound inequalities—treating the double inequality as two constraints that LL must satisfy simultaneously. The key insight is to isolate LL by performing the same operations on all three parts: add 2, then divide by 2.5. Once you have the range, you'll identify which whole numbers fall within it.

Intuitive explanation

This problem is about solving compound inequalities—treating the double inequality as two constraints that LL must satisfy simultaneously. The key insight is to isolate LL by performing the same operations on all three parts: add 2, then divide by 2.5. Once you have the range, you'll identify which whole numbers fall within it.

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