Inequalities

Students learn how to represent inequalities on a number line and solve an inequation using the balance method.

This unit takes place in Term 6 of Year 10 and follows on from solving equations.


Inequalities Lessons
Revision Lessons


Prerequisite Knowledge
  • order positive and negative integers
  • apply the four operations, including formal written methods, to integers, both positive and negative;
  • solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)

Success Criteria
  • solve linear inequalities in one variable;
  • represent the solution set on a number line;
  • understand and use the concepts and vocabulary of expressions, equations, formulae, identities and inequalities


Key Concepts
  • Knowledge of <,>, ≤ & ≥ notation is critical to this topic. Numbers which are less or greater than but not equal to are represented on a number line with a hollow circle. Full circles are used when an inequality can be equal to a number.
  • Inequations have a set of solutions whereas equations have distinct solutions.
  • Inequations can be solved using the balance method.
  • When dividing or multiplying both sides of an inequality by a negative number the sign is reversed.

Common Misconceptions
  • Students are often confused with the direction of the inequality sign. Use the number line to show < represents less than and > means greater than.
  • Inequalities such as 5 < x ≤ 10 represents x as any value greater than 5 and less than or equal to 10. Encourage students to read such inequalities in two directions i.e., 5 < x and x ≤ 10.

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