Inequality

Summary and Exam Tips for Inequality

Inequality is a subtopic of Algebra, which falls under the subject Mathematics in the IB MYP curriculum. Inequalities involve expressions that use symbols such as $>$, $<$, $\geq$, and $\leq$ to compare values. Solving inequalities is similar to solving equations, but with a key difference: when multiplying or dividing both sides by a negative number, the inequality sign must be reversed. For example, if you have $4 > -6$ and multiply both sides by $-2$, the inequality becomes $-8 < 12$.

To solve linear inequalities, move all variables to one side and constants to the other, using inverse operations as needed. Solutions can be represented on a number line, where closed circles indicate included values ($\geq$, $\leq$) and open circles indicate excluded values ($>$, $<$).

For inequalities involving two variables, such as $y > x - 5$, graphing on the Cartesian plane is useful. Quadratic inequalities, like $x^2 - 7x + 12 > 0$, require factoring and graphing to find solutions. The critical points are determined by setting the quadratic expression to zero, and the solution is found by analyzing the graph's position relative to the x-axis.

Exam Tips

• Understand the Symbols: Familiarize yourself with inequality symbols and their meanings to avoid confusion during exams.
• Reverse the Sign: Remember to reverse the inequality sign when multiplying or dividing by a negative number.
• Graph Solutions: Use number lines and Cartesian planes to visualize solutions, especially for quadratic inequalities.
• Practice Factorization: Ensure you can factor quadratic expressions, as this is crucial for solving quadratic inequalities.
• Check Your Work: Always verify your solutions by substituting them back into the original inequality to ensure they satisfy the condition.