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Linear equations

What are inequalities?

  • We are familiar with the use of the symbol \(=\) to mean what is on the left hand side equals that on the right hand side. 
  • If this is not so, that is, the left hand side does not equal the right hand side, then we use the symbol \(\ne \), meaning ‘not equal to’. For  example, we can say that \(7 \ne 3\) (read as \(7\) is not equal to \(3\)).
  • We can also use other symbols: 
    \(<\) Less than
    \(\leq\) Less than or equal to
    \(>\) Greater than
    \(\geq\) Greater than or equal to
  • We can graph inequations to help visualise their properties and solution.
  • The inequality \(x > 2\) is read as ‘\(x\) is greater than two’. We can represent this inequation on a real number line. 


  • Another example is: \(1 < x \leq 3\), read as '\(x\) is greater than one but less than or equal to three'. We can represent this inequality on a real number line as: