Study Notes
Inequalities involve expressions where one side is not equal to the other, using symbols like >, <, ≥, and ≤. Solving inequalities is similar to solving equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.
- More than (>) — indicates one value is greater than another. Example: x > 5 means "x is more than 5"
- Less than (<) — indicates one value is smaller than another. Example: y < 3 means "y is less than 3"
- More than or equal to (≥) — indicates one value is greater than or equal to another. Example: x ≥ 8 means "x is more than or equal to 8"
- Less than or equal to (≤) — indicates one value is smaller than or equal to another. Example: y ≤ 10 means "y is less than or equal to 10"
- Number line representation — used to show solutions of inequalities visually. Example: x < 4 is shown with an open circle at 4
- Graphical representation — used for inequalities with two variables on the Cartesian plane. Example: y > x - 5 is shown as a region above the line y = x - 5
- Quadratic inequalities — solved using graphs to find where the expression is above or below the x-axis. Example: x² - 7x + 12 > 0 is solved by finding critical points and sketching the graph
Exam Tips
Key Definitions to Remember
- More than (>)
- Less than (<)
- More than or equal to (≥)
- Less than or equal to (≤)
Common Confusions
- Forgetting to reverse the inequality sign when multiplying or dividing by a negative number
- Misinterpreting the inequality symbols
Typical Exam Questions
- Solve 4 - 2x < 2? Answer: x > 1
- Represent x < 4 on a number line? Answer: Open circle at 4, shading to the left
- Solve x² - 7x + 12 > 0? Answer: x < 3 or x > 4
What Examiners Usually Test
- Ability to solve linear inequalities
- Correct representation of solutions on a number line
- Understanding of how to graph inequalities with two variables
- Solving quadratic inequalities using graphs