Resources for Inequalities -Absolute Value
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Questions
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Video Tutorials
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Inequalities -Absolute Value Theory
NSW Y11 Maths - Extension 1 Functions Inequalities -Absolute Value
Videos
Videos relating to Inequalities -Absolute Value.
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Inequalities -Absolute Value - Video - Solving Absolute Value Equations and Inequalities - Number Line & Interval Notation
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Theory
For inequalities such as \(\left| {x - a} \right| \le x - b\), a graphical technique is the best method.
Let \(y = \left| {x - a} \right|\) 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 \(|ax+b| \ge k,\, |ax+b| \le k,\, |ax+b| <k\) and \(|ax+b| > k\)