MathematicsExam code: 0580

Linear Equations and Inequalities

Algebra and Sequences

PractiseFlashcards

The conventions

  • The specification fixes how end points are drawn, and marks are given for using them correctly
  • An open circle marks a strict end point, which is excluded
  • A closed circle marks an inclusive end point, which is included
  • A line joins two end points, and an arrow shows an unbounded direction
A number line in t from −5 to 5 with an open circle at 3 and an arrow running from it off the left-hand end, representing every value below 3 with no lower limit
Source: Solving linear inequalities by Save My Exams
Number line from −5 to 5 with an open circle at −3 joined by a solid line to a closed circle at 4, representing all values greater than −3 and less than or equal to 4
Source: Representing inequalities on a number line by Save My Exams
  • The diagram above represents −3 < x ⩽ 4
A number line from −5 to 5 with a closed circle at −2 joined to an open circle at 1, representing all values from −2 up to but not including 1
Source: Solving linear inequalities by Save My Exams

Worked example

Reading a solution off a number line

A number line has a closed circle at −1 and an open circle at 4, with the line between them shaded. Write down the inequality it represents.

A number line from −3 to 6 labelled x, with a filled circle at −1, an open circle at 4 and a thick line joining them

Solution:

  • Take each end in turn, using the circle to fix the symbol
  • The closed circle at −1 means −1 is included, so that end uses ⩽
  • The open circle at 4 means 4 is excluded, so that end uses <
  • The shading lies between them, so x is between the two values
  • The inequality is −1 ⩽ x < 4
  • Written the other way round it reads 4 > x ⩾ −1, which says the same thing

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