Solve |linear| > constant (greater than)

Solve inequality where modulus of linear expression is strictly greater than or greater than or equal to a positive constant, e.g. |2x-7| > 3 or |3x+1| ≥ 8.

10 questions · Easy -1.1

1.02l Modulus function: notation, relations, equations and inequalities
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CAIE P2 2006 June Q1
3 marks Easy -1.2
1 Solve the inequality \(| 2 x - 7 | > 3\).
CAIE P2 2010 June Q1
3 marks Easy -1.2
1 Solve the inequality \(| 2 x - 3 | > 5\).
CAIE P2 2010 November Q1
3 marks Easy -1.2
1 Solve the inequality \(| 3 x + 1 | > 8\).
OCR MEI C3 Q4
4 marks Easy -1.2
4 Solve the inequality \(| 2 x + 1 | \geqslant 4\).
OCR MEI C3 2012 June Q2
3 marks Easy -1.2
2 Solve the inequality \(| 2 x + 1 | > 4\).
OCR MEI Paper 1 Specimen Q3
4 marks Easy -1.2
3 Solve the inequality \(| 2 x - 1 | \geq 4\).
OCR MEI Paper 3 2020 November Q2
4 marks Moderate -0.8
2 The graph of \(y = | 1 - x | - 2\) is shown in Fig. 2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a13f7a05-e2d3-4354-a0c7-ef7283eff514-04_625_1102_794_242} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Determine the set of values of \(x\) for which \(| 1 - x | > 2\).
AQA C3 2010 January Q4
6 marks Moderate -0.8
4
  1. Sketch the graph of \(y = | 8 - 2 x |\).
  2. Solve the equation \(| 8 - 2 x | = 4\).
  3. Solve the inequality \(| 8 - 2 x | > 4\).
OCR MEI C3 2011 January Q2
4 marks Moderate -0.8
Solve the inequality \(|2x + 1| \geqslant 4\). [4]
SPS SPS FM Pure 2023 June Q1
5 marks Easy -1.2
You are given that \(gf(x) = |3x - 1|\) for \(x \in \mathbb{R}\).
  1. Given that \(f(x) = 3x - 1\), express \(g(x)\) in terms of \(x\). [1]
  2. State the range of \(gf(x)\). [1]
  3. Solve the inequality \(|3x - 1| > 1\). [3]