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 where two values are compared using symbols such as $>$, $<$, $\geq$, and $\leq$. Solving inequalities is similar to solving equations, with the key difference being that when you multiply or divide by a negative number, the inequality sign reverses. For example, $4 > -6$ becomes $-8 < 12$ when multiplied by $-2$.

To solve inequalities, follow these steps:

• Move all variables to one side and constants to the other.
• Use inverse operations to simplify.
• Reverse the inequality sign when multiplying or dividing by a negative.

Graphical representation can be used for linear inequalities with two variables, such as $y > x - 5$. For quadratic inequalities like $x^2 - 7x + 12 > 0$, factorize the quadratic equation, find critical points, and sketch the graph to determine the solution area. Solutions can also be represented on a number line, indicating whether endpoints are included ($\geq$, $\leq$) or not ($>$, $<$).

Exam Tips

• Understand Symbols: Familiarize yourself with inequality symbols and their meanings. This is crucial for interpreting and solving problems correctly.
• Reverse the Sign: Always remember to reverse the inequality sign when multiplying or dividing by a negative number.
• Graphing Skills: Practice sketching graphs for inequalities, especially for quadratic ones, to visualize solutions effectively.
• Use Number Lines: Represent solutions on a number line to clearly see the range of possible values.
• Practice Problems: Solve various practice questions to strengthen your understanding and application of inequalities in different contexts.