Linear Inequalities (Edexcel AS Maths) : Revision Note

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Linear Inequalities

What are linear inequalities?

  • Linear inequalities are 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

  • Inequalities use the symbols following symbols

    • greater thanGreater than e.g. 5 space greater than space 3

    • less thanLess than e.g. negative 8 space less than space 7

    • greater or equal than Greater than or equal to

    • less or equal thanLess than or equal to

  • Inequalities can be represented in many ways using number lines, set notation and interval notation

2.4.1 Linear Inequalities Notes Diagram 4, Edexcel A Level Maths: Pure revision notes

Number line diagrams 

  • Number line diagrams are made up from circles and lines set above a number line

    • A filled-in circle or empty circle above a number denotes whether the number is included or not

      • filled in for the greater/less than or equal to symbols

      • empty for the greater/less than symbols

    • Arrows show the range of values that are allowed

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

Set notation

  • Set notation is a formal way of writing a range of values

  • Use of curly brackets { }

  • Intersection ∩ and union ∪ may be used

  • Not to be confused with interval notation

2.4.1 Linear Inequalities Notes Diagram 2, Edexcel A Level Maths: Pure revision notes

Interval notation

  • Interval notation uses different brackets to indicate whether a number is included or not

  • Use of square [] and round () brackets

  • [ or ] mean included

  • ( or ) mean excluded

    • (4,8] means 4 < x < 8

  • Note ∞ always uses ( or )

  • Not to be confused with set notation

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

 

Skills for solving linear inequalities

  • representing and interpreting inequalities displayed on a number line

  • writing and interpreting set notation

    • eg {x : x > 1} ∩ {x : x ≤ 7} is the same as 1 < x ≤ 7

  • writing and interpreting interval notation

    • eg [-4, 6) is the same as -4 ≤ x < 6

How do I solve linear inequalities?

  • Treat the inequality as an equation and solve

    • avoid multiplying or dividing by a negative

    • if unavoidable, “flip” the inequality sign so < → >, ≥ → ≤, etc

    • try to rearrange to make the x term positive

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

Worked Example

2.4.1 Linear Inequalities Example Diagram, Edexcel A Level Maths: Pure revision notes
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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

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.

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