Study Notes
Number lines and inequalities are tools used to represent and solve mathematical expressions involving comparisons. Inequalities can be solved similarly to equations, with special rules for reversing the inequality sign when multiplying or dividing by a negative number.
- 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"
- Number line — a visual representation of numbers where inequalities can be shown. Example: x < 4 is shown with an open circle at 4 and shading to the left
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
- Mixing up the symbols for more than and less than
Typical Exam Questions
- Solve 4 - 2x < 2? Answer: x > 1
- Solve 2(x + 1) > x - 7? Answer: x > -9
- Match the inequality x < 4 to its number line? Answer: Open circle at 4, shading to the left
What Examiners Usually Test
- Ability to solve inequalities correctly
- Correct representation of inequalities on a number line
- Understanding of when to reverse the inequality sign