Inequalities
Understanding Inequalities
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An inequality shows the relationship between two expressions that may not be equal.
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The symbols used in inequalities are > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), ≠ (not equal to).
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A number line can be used to visualise an inequality.
Solving Inequalities
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You can solve inequalities in the same way you solve equations.
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When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number.
Graphical Representation of Inequalities
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Inequalities can be represented graphically on number lines or coordinate grids.
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An open circle on a number line represents a 'less than' or 'greater than' inequality.
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A closed circle on a number line represents a 'less than or equal to' or 'greater than or equal to' inequality.
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To represent an inequality on a coordinate grid, use a dashed line for 'less than' or 'greater than', and a solid line for 'less than or equal to' or 'greater than or equal to'.
Inequalities with More Than One Variable
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When dealing with inequalities with more than one variable, use similar techniques as with equations.
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Remember to make one variable the subject first if the inequality does not involve a straight-line equation.
Solving Inequalities Involving Absolute Values
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The absolute value of a number is its distance from zero.
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Solving inequalities involving absolute values consists of two steps: solving the equation where the absolute value is greater, then where it is less.
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Simplification methods are used to split the inequality into two separate inequalities based on the absolute value.
Inequalities and Real-Life Situations
- Inequalities are widely used to represent real-life situations. For example, they can be used to describe the minimum or maximum limits on things like speed, weight, costs, etc.