Every member of the community library may take out \(n\) music DVDs at one time. Here \(n\) is a whole number satisfying both \(2n + 3 > 7\) and \(n < 6\). ...
Question 1 Report
Every member of the community library may take out \(n\) music DVDs at one time. Here \(n\) is a whole number satisfying both \(2n + 3 > 7\) and \(n < 6\). Write down all the possible values of \(n\). (2)
Answer Details
Two conditions must hold at the same time, so solve the first inequality and then read off the whole numbers that also satisfy the second.
- \(2n+3 > 7\). Subtract 3 from both sides: \(2n > 4\). Divide by 2 (a positive number, so the inequality sign is unchanged): \(n > 2\). [1]
- Combining \(n > 2\) with \(n < 6\) gives \(2 < n < 6\). Because \(n\) is a whole number and both ends are strict, 2 and 6 are excluded, leaving \(n = 3, 4, 5\). [1]
So a member may take out 3, 4 or 5 DVDs.
The question asks for the values themselves, not the range, so an answer of \(2 < n < 6\) alone is incomplete. The most common error is including the end points: a strict \(>\) or \(<\) never allows the boundary value, whereas \(\geqslant\) or \(\leqslant\) would.
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