Mathematics (Foundation)
Algebra
Inequalities
🤓 Study
📖 Quiz
Play audio lesson
Inequalities
Understanding Inequalities

An inequality shows the relationship between two expressions that may not be equal.

The symbols used in inequalities are > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), ≠ (not equal to).

A number line can be used to visualise an inequality.
Solving Inequalities

You can solve inequalities in the same way you solve equations.

When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number.
Graphical Representation of Inequalities

Inequalities can be represented graphically on number lines or coordinate grids.

An open circle on a number line represents a 'less than' or 'greater than' inequality.

A closed circle on a number line represents a 'less than or equal to' or 'greater than or equal to' inequality.

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

When dealing with inequalities with more than one variable, use similar techniques as with equations.

Remember to make one variable the subject first if the inequality does not involve a straightline equation.
Solving Inequalities Involving Absolute Values

The absolute value of a number is its distance from zero.

Solving inequalities involving absolute values consists of two steps: solving the equation where the absolute value is greater, then where it is less.

Simplification methods are used to split the inequality into two separate inequalities based on the absolute value.
Inequalities and RealLife Situations
 Inequalities are widely used to represent reallife situations. For example, they can be used to describe the minimum or maximum limits on things like speed, weight, costs, etc.