Linear Equations Made Easy
Step-by-Step Study Guide (One Variable)
Quick Notes • Worked Examples • Practice • Exam Tips
1. What Is a Linear Equation?
A linear equation in one variable is an equation that:
• Contains only ONE unknown letter (the variable, usually x).
• Has the variable raised only to the power of 1 (no x², √x, or 1/x).
• Has exactly one solution.
In simple words:
It's an equation where you're solving for one unknown number, and the answer is a single value
that makes both sides equal.
2. The Standard Form
ax + b = 0
Where:
• a → the coefficient of x (any number, but not zero).
• b → the constant term (any number, including 0).
• x → the unknown variable you want to find.
Example: In 3x + 6 = 0, a = 3 and b = 6.
3. Step-by-Step Method
Follow these 4 steps every time:
1. Simplify both sides — open brackets and combine like terms.
2. Move variables to one side and constants to the other (change the sign when crossing the = sign).
3. Combine like terms on each side.
4. Divide both sides by the coefficient of x to get x alone.
Golden Rule
Whatever you do to one side, you must do to the other side — keep the equation balanced!
4. Worked Examples
Example 1: Solve x + 7 = 12
Subtract 7 from both sides → x = 12 − 7
Simplify → x = 5
Answer: x = 5
Example 2: Solve 3x − 4 = 11
Step-by-Step Study Guide (One Variable)
Quick Notes • Worked Examples • Practice • Exam Tips
1. What Is a Linear Equation?
A linear equation in one variable is an equation that:
• Contains only ONE unknown letter (the variable, usually x).
• Has the variable raised only to the power of 1 (no x², √x, or 1/x).
• Has exactly one solution.
In simple words:
It's an equation where you're solving for one unknown number, and the answer is a single value
that makes both sides equal.
2. The Standard Form
ax + b = 0
Where:
• a → the coefficient of x (any number, but not zero).
• b → the constant term (any number, including 0).
• x → the unknown variable you want to find.
Example: In 3x + 6 = 0, a = 3 and b = 6.
3. Step-by-Step Method
Follow these 4 steps every time:
1. Simplify both sides — open brackets and combine like terms.
2. Move variables to one side and constants to the other (change the sign when crossing the = sign).
3. Combine like terms on each side.
4. Divide both sides by the coefficient of x to get x alone.
Golden Rule
Whatever you do to one side, you must do to the other side — keep the equation balanced!
4. Worked Examples
Example 1: Solve x + 7 = 12
Subtract 7 from both sides → x = 12 − 7
Simplify → x = 5
Answer: x = 5
Example 2: Solve 3x − 4 = 11
