Solve |linear| < constant with sketch or follow-up application

Solve |ax+b| < c or |ax+b| ≤ c where a sketch is required first, or there is a follow-up part applying the result (e.g. finding integers satisfying the inequality or deducing a result involving logarithms or other functions).

4 questions · Moderate -0.4

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CAIE P2 2023 November Q4
9 marks Moderate -0.3
4
  1. Sketch, on the same diagram, the graphs of \(y = | 3 - x |\) and \(y = 9 - 2 x\).
  2. Solve the inequality \(| 3 - x | > 9 - 2 x\).
  3. Use logarithms to solve the inequality \(2 ^ { 3 x - 10 } < 500\). Give your answer in the form \(x < a\), where the value of \(a\) is given correct to 3 significant figures.
  4. List the integers that satisfy both of the inequalities \(| 3 - x | > 9 - 2 x\) and \(2 ^ { 3 x - 10 } < 500\).
OCR C3 Q1
5 marks Standard +0.3
  1. (i) Solve the inequality
$$| x - 0.2 | < 0.03$$ (ii) Hence, find all integers \(n\) such that $$\left| 0.95 ^ { n } - 0.2 \right| < 0.03$$
OCR MEI C3 Q2
4 marks Moderate -0.8
2
  1. Sketch the graph of \(y = | 2 x - 3 |\).
  2. Hence, or otherwise, solve the inequality \(| 2 x - 3 | < 5\). Illustrate your answer on your graph.
OCR MEI Paper 3 2023 June Q2
4 marks Moderate -0.8
2 The straight line \(y = 5 - 2 x\) is shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{20639e13-01cc-4d96-b694-fb3cf1828f4d-04_705_773_881_239}
  1. On the copy of the diagram in the Printed Answer Booklet, sketch the graph of \(y = | 5 - 2 x |\).
  2. Solve the inequality \(| 5 - 2 x | < 3\).