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NSW Y11 Maths Standard NSW Y11 Maths Advanced NSW Y11 Maths Extension 1

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NSW Y11 Maths - Extension 1 Functions Inequalities -Absolute Value

Resources for Inequalities -Absolute Value

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Inequalities -Absolute Value Theory

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Videos relating to Inequalities -Absolute Value.

  • Inequalities -Absolute Value - Video - Solving Absolute Value Equations and Inequalities - Number Line & Interval Notation

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Theory

For inequalities such as |x−a|≤x−b, a graphical technique is the best method.

Let y=|x−a| and y=x−b, draw the graphs and then calculate the points of intersection. These points will be the critical points, which will determine the regions where the inequality is valid.

Syllabus Reference

NSW Syllabus Reference: ME-F1.2 Inequalities. This will require student to 

  • solve quadratic inequalities using both algebraic and graphical techniques
  • solve inequalities involving rational expressions, including those with the unknown in the denominator
  • solve absolute value inequalities of the form |ax+b|≥k,|ax+b|≤k,|ax+b|<k and |ax+b|>k

Ref: https://educationstandards.nsw.edu.au/