# 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.

##### 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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