Study Notes
Number lines and inequalities are tools used to represent and solve mathematical relationships involving numbers.
- Number Line — a visual representation of numbers on a straight line. Example: A number line can show the solution to x < 4 by marking all points to the left of 4.
- Inequality — a mathematical statement that shows the relationship between two values where they are not equal. Example: x > 5 means x is more than 5.
- More than — indicates a value is greater than another. Example: x > 5 means “x is more than 5”.
- Less than — indicates a value is smaller than another. Example: y < 3 means “y is less than 3”.
- More than or equal to — indicates a 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 a value is smaller than or equal to another. Example: y ≤ 10 means “y is less than or equal to 10”.
Exam Tips
Key Definitions to Remember
- Number Line
- Inequality
- 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
- Mixing up the symbols for more than (>) and less than (<)
Typical Exam Questions
- Solve 4 - 2x < 2? 1 < x
- Solve 2(x + 1) > x - 7? x > -9
- Match the inequality to its number line representation? Use the number line to show solutions like x < 4
What Examiners Usually Test
- Ability to solve inequalities and represent them on a number line
- Understanding of inequality symbols and their meanings
- Correct application of rules when solving inequalities, especially with negative numbers