The answer
(a) \(3 < x \leqslant 8.5\)
(b) \(4, 5, 6, 7, 8\)
O-Level E-Math 2015 Paper 1 Question 15 · Verified worked solution by the Genius Plus Academy teaching team
The question
(a) Solve the inequalities \(-10 \leqslant 7 - 2x < 1\). [2]
(b) Write down all the integers that satisfy \(-10 \leqslant 7 - 2x < 1\). [1]
(a) Subtract 7 throughout: \(-17 \leqslant -2x < -6\). Divide by \(-2\) and reverse both inequality signs: \(8.5 \geqslant x > 3\), i.e. \(3 < x \leqslant 8.5\).
(b) The integers strictly greater than 3 and at most 8.5 are \(4, 5, 6, 7, 8\).
Answer: (a) \(3 < x \leqslant 8.5\)
(b) \(4, 5, 6, 7, 8\)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a solve a double linear inequality question from Equations & inequalities, worth 3 marks: 2 + 1.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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