Study Notes
In algebra, equations and inequalities are fundamental concepts that involve finding the value of unknown variables. Equations are mathematical statements that assert the equality of two expressions, while inequalities show the relationship of one expression being greater or less than another.
- Equation — a statement that asserts the equality of two expressions.
Example: 7z - (3z - 4) = 12 simplifies to z = 2. - Inequality — a statement that compares two expressions, showing if one is greater, less, or equal to the other.
Example: 4 - 2x < 2 simplifies to x > 1. - Simultaneous Equations — a set of equations with multiple unknowns that are solved together.
Example: Solving 3x + y = 19 and x + y = 9 gives x = 5 and y = 4. - More than (>) — indicates that one value is greater than another.
Example: x > 5 means "x is more than 5". - Less than (<) — indicates that one value is less than another.
Example: y < 3 means "y is less than 3".
Exam Tips
Key Definitions to Remember
- An equation asserts the equality of two expressions.
- An inequality compares two expressions, showing if one is greater, less, or equal to the other.
- Simultaneous equations involve solving multiple equations together.
Common Confusions
- Forgetting to reverse the inequality sign when multiplying or dividing by a negative number.
- Mixing up the symbols for inequalities (e.g., using > instead of <).
Typical Exam Questions
- How do you solve 7z - (3z - 4) = 12? Simplify to find z = 2.
- Solve the inequality 4 - 2x < 2. Simplify to find x > 1.
- What are the solutions to the simultaneous equations 3x + y = 19 and x + y = 9? x = 5 and y = 4.
What Examiners Usually Test
- Ability to simplify and solve linear equations.
- Understanding of how to solve and represent inequalities.
- Skill in solving simultaneous equations and interpreting solutions.