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Maths Gcse Edexcel Foundation

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Exam code:1MA1

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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