Study Notes
Inequalities involve comparing two expressions using symbols to show if one is greater, less, or equal to the other. Solving inequalities is similar to solving equations but requires special attention when multiplying or dividing by negative numbers.
- Greater than (>) — indicates one value is more than another. Example: x > 5 means "x is more than 5."
- Less than (<) — indicates one value is less than another. Example: y < 3 means "y is less than 3."
- Greater than or equal to (≥) — indicates one value is more 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 less than or equal to another. Example: y ≤ 10 means "y is less than or equal to 10."
- Number line representation — used to visually show solutions of inequalities. Example: x < 4 is shown with an open circle at 4.
- Graphical representation — used for inequalities with two variables on a Cartesian plane. Example: y > x - 5 is shown as a shaded region above the line y = x - 5.
- Quadratic inequalities — solved using graphs to determine where the function 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
- Greater than (>)
- Less than (<)
- Greater 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
- Misrepresenting solutions on a number line
Typical Exam Questions
- Solve 4 - 2x < 2? x > 1
- Represent x ≥ -2 on a number line? Closed circle at -2, shading to the right
- Solve x² - 7x + 12 > 0 using a graph? x < 3 and x > 4
What Examiners Usually Test
- Ability to solve linear inequalities
- Correct representation of solutions on number lines
- Understanding of how to graph inequalities with two variables
- Solving quadratic inequalities using graphs