Solve |linear| < |linear|

Solve an inequality comparing two modulus of linear expressions, e.g. |3x-7| < |4x+5|.

23 questions · Standard +0.3

1.02l Modulus function: notation, relations, equations and inequalities
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CAIE P2 2021 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| 3 x - 7 | < | 4 x + 5 |\).
CAIE P2 2002 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| x + 2 | < | 5 - 2 x |\).
CAIE P2 2009 June Q2
4 marks Standard +0.3
2 Solve the inequality \(| 3 x + 2 | < | x |\).
CAIE P2 2010 June Q3
4 marks Standard +0.3
3 Solve the inequality \(| 2 x - 1 | < | x + 4 |\).
CAIE P2 2012 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| x + 3 | < | 2 x + 1 |\).
CAIE P2 2018 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| 3 x - 2 | < | x + 5 |\).
CAIE P3 2004 June Q2
4 marks Standard +0.3
2 Solve the inequality \(| 2 x + 1 | < | x |\).
CAIE P3 2011 June Q1
3 marks Standard +0.3
1 Solve the inequality \(| x | < | 5 + 2 x |\).
CAIE P3 2014 November Q1
4 marks Standard +0.3
1 Solve the inequality \(| 3 x - 1 | < | 2 x + 5 |\).
CAIE P2 2019 June Q2
6 marks Standard +0.3
2
  1. Solve the inequality \(| 3 x - 5 | < | x + 3 |\).
  2. Hence find the greatest integer \(n\) satisfying the inequality \(\left| 3 ^ { 0.1 n + 1 } - 5 \right| < \left| 3 ^ { 0.1 n } + 3 \right|\).
CAIE P2 2016 March Q2
4 marks Standard +0.3
2 Solve the inequality \(| x - 5 | < | 2 x + 3 |\).
CAIE P2 2017 March Q3
6 marks Standard +0.3
3
  1. Solve the inequality \(| 2 x - 5 | < | x + 3 |\).
  2. Hence find the largest integer \(y\) satisfying the inequality \(| 2 \ln y - 5 | < | \ln y + 3 |\).
CAIE P2 2002 November Q1
4 marks Standard +0.3
1 Solve the inequality \(| 2 x - 1 | < | 3 x |\).
CAIE P2 2009 November Q1
4 marks Standard +0.3
1 Solve the inequality \(| 2 x + 3 | < | x - 3 |\).
CAIE P2 2012 November Q1
3 marks Standard +0.3
1 Solve the inequality \(| 2 x + 1 | < | 2 x - 5 |\).
CAIE P2 2013 November Q1
4 marks Standard +0.3
1 Solve the inequality \(| x + 1 | < | 3 x + 5 |\).
CAIE P2 2019 November Q1
5 marks Standard +0.3
1
  1. Solve the inequality \(| 2 x - 7 | < | 2 x - 9 |\).
  2. Hence find the largest integer \(n\) satisfying the inequality \(| 2 \ln n - 7 | < | 2 \ln n - 9 |\).
OCR C3 2006 June Q2
5 marks Standard +0.3
2 Solve the inequality \(| 2 x - 3 | < | x + 1 |\).
OCR C3 2007 June Q2
5 marks Standard +0.3
2 Solve the inequality \(| 4 x - 3 | < | 2 x + 1 |\).
Pre-U Pre-U 9794/1 2017 June Q5
5 marks Standard +0.3
5 Solve \(| x - \sqrt { 3 } | < | x + 2 \sqrt { 3 } |\) giving the answer in exact form.
OCR C3 2013 January Q3
7 marks Standard +0.8
  1. Given that \(|t| = 3\), find the possible values of \(|2t - 1|\). [3]
  2. Solve the inequality \(|x - t^2| > |x + 3\sqrt{2}|\). [4]
OCR C3 2010 June Q5
7 marks Standard +0.8
  1. Solve the inequality \(|2x + 1| \leqslant |x - 3|\). [5]
  2. Given that \(x\) satisfies the inequality \(|2x + 1| \leqslant |x - 3|\), find the greatest possible value of \(|x + 2|\). [2]
OCR H240/03 2019 June Q3
7 marks Moderate -0.3
  1. In this question you must show detailed reasoning. Solve the inequality \(|x - 2| \leqslant |2x - 6|\). [4]
  2. Give full details of a sequence of two transformations needed to transform the graph of \(y = |x - 2|\) to the graph of \(y = |2x - 6|\). [3]