IGCSEMathsCambridge (CIE)International MathsCoreRevision NotesAlgebra & SequencesInequalitiesRepresenting Inequalities on a Number Line

Representing Inequalities on a Number Line (Cambridge (CIE) IGCSE International Maths)

Revision Note

Mark Curtis

Expertise

Maths

Representing Inequalities on a Number Line

How do I represent an inequality on a number line?

  • The inequality -3 < x ≤ 4 is shown on a number line below

A number line representing an inequality

  • Draw circles above the end points and connect them with a horizontal line

    • Leave an open circle for end points with strict inequalities, < or >

      • These end points are not included

    • Fill in a solid circle for end points with ≤ or ≥ inequalities

      • These end points are included

        open circles when not including the ends, closed circles when including the ends

  • Use a horizontal arrow for inequalities with one end point

    • x > 5 is an open circle at 5 with a horizontal arrow pointing to the right 

Worked Example

Represent the following inequalities on a number line.

(a) negative 2 less or equal than x less than 1

-2 is included so use a closed circle

1 is not included so use an open circle

Number line from -2 to 1, not including -2

(b) t less than 3

3 is not included so use an open circle

There is no second end point
Any value less than three is accepted, so draw a horizontal arrow to the left

Number line for t < 3

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    Mark Curtis

    Author: Mark Curtis

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.