Inequalities and Inequations

Students learn how to solve inequations and represent their solutions on a number line using the correct notation and symbols.  As learning progress they move on plotting inequalities on a grid and solving inequations involving quadratics.

This unit takes place in and follows on from solving equations.


Inequalities and Inequations Lessons
Revision Lessons


Prerequisite Knowledge
  • Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)
  • Plot graphs of equations that correspond to straight-line graphs in the coordinate plane;
  • Identify and interpret gradients and intercepts of linear functions graphically and algebraically

Success Criteria
  • Solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable;
  • Represent a solution set on a number line, using set notation and on a graph


Key Concepts
  • When representing inequalities on a grid it is easier to plot the straight line first and then decide which side to shade.
  • Students need to have a secure understanding of the <, >, ≥, and ≤ notation for defining inequalities.
  • When multiplying or dividing an inequality by -1 the sign changes.
  • Solid boundary lines do include the value on the line. Dashed boundary lines do not.

Common Misconceptions
  • Students tend to not interpret the “≤” and “<” signs correctly
  • Confusion often lies in understanding the notation using empty and full circles on a number line.
  • Inequations are solved as individual values rather than sets.
  • Students often find it difficult to identify the correct region for linear and quadratic inequalities on a grid.

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