Linear Equations with One Variable
A linear equation with one variable is one of the most fundamental concepts in algebra. Understanding how to solve these equations opens the door to more advanced mathematics.
📚 Definition
Linear Equation with One Variable: An equation that can be written in the form ax + b = 0 or ax = b, where:
- a and b are numbers (constants)
- x is the variable (unknown)
- a ≠ 0 (coefficient of x cannot be zero)
- The highest power of the variable is 1
Examples of Linear Equations:
- 3x − 6 = 0
- 2x + 5 = 11
- 5x = 15
- x/2 + 3 = 7
📐 Why Called "Linear"?
The word "linear" comes from the Latin word "linea" meaning line.
Key Reasons:
- The graph of y = ax + b is a straight line
- The degree (power) of the variable is 1 (first-degree equation)
- It's the simplest type of algebraic equation
Interactive visualization — available in the full lesson
The graph of a linear equation is always a straight line!
📋 Standard Form
ax + b = 0
where a ≠ 0
- a = coefficient of the variable
- b = constant term
- x = variable (unknown)
Important: Any linear equation can be transformed to this standard form!
| Original Equation | Standard Form |
|---|---|
| 2x + 5 = 11 | 2x − 6 = 0 |
| 3x = 15 | 3x − 15 = 0 |
| x − 7 = 2 | x − 9 = 0 |