Inequalities

Summary and Exam Tips for Inequalities

Inequalities is a subtopic of Equations, Formulae, and Identities, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. Inequalities involve mathematical expressions using symbols such as $<$, $>$, $\leq$, and $\geq$. Solving an inequality means determining the range of values that satisfy the inequality condition. For example, $x > 5$ indicates that $x$ is more than 5, while $y \leq 10$ means $y$ is less than or equal to 10.

To solve linear inequalities, you can manipulate the inequality similar to equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number. Solutions can be represented on a number line for one variable or as a region on a Cartesian plane for two variables. For instance, solving $4 - 2x < 2$ results in $x > 1$, and this can be shown on a number line. Similarly, inequalities with two variables, like $y > x + 5$, can be graphed to show the solution region. Practice problems and past paper questions are essential for mastering this topic.

Exam Tips

• Understand the Symbols: Familiarize yourself with inequality symbols and their meanings. This will help you interpret and solve problems accurately.
• Reverse the Sign: Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.
• Graphical Representation: Practice representing inequalities on a number line and graphing them on a Cartesian plane, especially for two-variable inequalities.
• Word Problems: Practice forming inequalities from word problems to enhance your problem-solving skills.
• Check Solutions: After solving, substitute values back into the original inequality to verify your solutions.