Study Notes
Inequalities are mathematical expressions that show the relationship between two values using symbols like <, >, ≤, and ≥. Solving an inequality involves finding the range of values that satisfy the inequality.
- Inequality — a mathematical statement that compares two expressions using inequality symbols. Example: x > 5 means "x is more than 5."
- Linear Inequality — an inequality that involves a linear expression. Example: 4 - 2x < 2 can be solved to find x.
- Number Line Representation — a way to visually show the solutions of an inequality. Example: x > 1 is shown with an open circle at 1 and shading to the right.
- Graphical Representation — using a graph to show solutions of inequalities with two variables. Example: y > x + 5 is represented as a region above the line y = x + 5.
Exam Tips
Key Definitions to Remember
- Inequality symbols: <, >, ≤, ≥
- Linear inequality: an inequality involving a linear expression
Common Confusions
- Forgetting to reverse the inequality symbol when multiplying or dividing by a negative number
- Misinterpreting the inequality symbols
Typical Exam Questions
- Solve 4 - 2x < 2? x > 1
- Represent y > x + 5 on a graph? Shade the region above the line y = x + 5
- List the integer solutions of 3 ≤ 3x < x + 6? x = 1
What Examiners Usually Test
- Ability to solve linear inequalities
- Correct representation of solutions on a number line or graph
- Understanding of inequality symbols and their meanings