Solve |linear| compared to linear: algebraic only

Solve inequality or equation comparing modulus of linear expression to a non-modulus linear expression using algebra, without requiring a sketch.

12 questions · Moderate -0.2

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CAIE P2 2022 November Q1
4 marks Moderate -0.5
1 Solve the inequality \(| 2 x - 5 | > x\).
CAIE P2 2024 November Q2
4 marks Standard +0.3
2 Solve the inequality \(| x - 7 | > 4 x + 3\).
CAIE P3 2003 June Q3
4 marks Standard +0.3
3 Solve the inequality \(| x - 2 | < 3 - 2 x\).
CAIE P3 2015 June Q2
4 marks Moderate -0.5
2 Solve the inequality \(| x - 2 | > 2 x - 3\).
CAIE P3 2009 November Q1
4 marks Moderate -0.3
1 Solve the inequality \(2 - 3 x < | x - 3 |\).
Edexcel FP2 2002 June Q1
5 marks Moderate -0.5
  1. Find the set of values for which
$$| x - 1 | > 6 x - 1$$
OCR H240/03 Q1
7 marks Standard +0.3
1
  1. If \(| x | = 3\), find the possible values of \(| 2 x - 1 |\).
  2. Find the set of values of \(x\) for which \(| 2 x - 1 | > x + 1\). Give your answer in set notation.
AQA Paper 1 2020 June Q4
5 marks Easy -1.2
4
  1. Sketch the graph of \includegraphics[max width=\textwidth, alt={}, center]{08e1f291-7052-40a5-b7b2-13fd1d0137c2-04_933_1093_349_475} 4
  2. Solve the inequality $$4 - | 2 x - 6 | > 2$$
CAIE P3 2006 June Q2
4 marks Moderate -0.3
Solve the inequality \(2x > |x - 1|\). [4]
Edexcel FP2 Q1
5 marks Moderate -0.3
Find the set of values for which $$|x - 1| > 6x - 1.$$ [5]
AQA Further Paper 1 2023 June Q7
5 marks Standard +0.8
The function f is defined by $$f(x) = \left|\sin x + \frac{1}{2}\right| \quad (0 \leq x \leq 2\pi)$$ Find the set of values of \(x\) for which $$f(x) \geq \frac{1}{2}$$ Give your answer in set notation. [5 marks]
OCR H240/03 2017 Specimen Q1
7 marks Moderate -0.3
  1. If \(|x| = 3\), find the possible values of \(|2x - 1|\). [3]
  2. Find the set of values of \(x\) for which \(|2x - 1| > x + 1\). Give your answer in set notation. [4]