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ASMaths: Pure 1CIERevision Notes1. Algebra & Functions1.2 Inequalities & Simultaneous Equations1.2.4 Linear Inequalities

Linear Inequalities (CIE AS Maths: Pure 1)

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Linear Inequalities

Linear inequalities

  • Similar to equations but answers take a range of values
  • Linear means there will be no terms other than degree 1
    • no squared terms or higher powers, no fractional or negative powers
  • Number line diagrams are often used

2.4.1 Linear Inequalities Notes Diagram 1, Edexcel A Level Maths: Pure revision notes

 

Interval notation

  • Use of square [] and round () brackets
  • [ or ] mean included
  • ( or ) mean excluded
    • (4,8] means 4 < x < 8
  • Note ∞ always uses ( or )

2.4.1 Linear Inequalities Notes Diagram 3, Edexcel A Level Maths: Pure revision notes 

How do I solve linear inequalities?

  • treat as equations but
    • avoid multiplying or dividing by a negative
    • if unavoidable, “flip” the inequality sign so < → >, ≥ → ≤, etc
    • do rearrange to make the x term positive

2.4.1 Linear Inequalities Notes Diagram 5, Edexcel A Level Maths: Pure revision notes

Worked example

1-2-4-linear-inequalities-example-diagram

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    Paul

    Author: Paul

    Expertise: Maths

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.