At a community library, the number of books \(x\) a member may currently have out on loan before a friendly reminder letter is posted through their door eac...
Question 1 Report
At a community library, the number of books \(x\) a member may currently have out on loan before a friendly reminder letter is posted through their door each half term satisfies \(2x - 5 \leq 9\). Solve this inequality to find the greatest possible integer value of \(x\). (2)
Answer Details
Solving a linear inequality follows the same steps as solving an equation, keeping the inequality sign unchanged since only positive numbers are involved here; the greatest integer satisfying "less than or equal to" a value is simply that value if it is a whole number.
Adding 5 to both sides: \(2x \leqslant 14\). Dividing by 2: \(x \leqslant 7\). [1 mark]
Since 7 itself satisfies \(x\leqslant7\), the greatest possible integer value of \(x\) is \(7\). [1 mark]
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