Linear Equations in One Variable
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- A linear equation in one variable has one variable with highest power 1.
- Equality must be preserved by performing equivalent operations on both sides.
- Collect variable terms on one side and constants on the other.
- Remove brackets carefully and clear fractions when helpful.
- Always check the final value in the original equation.
What You Will Learn
- Identify a linear equation in one variable
- Solve equations by balancing or transposition
- Solve equations with brackets and fractions
- Handle variables on both sides
- Form equations from word problems and check solutions
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Core idea
An equation states that two expressions are equal. Solving an equation means finding the value of the variable that makes the statement true. Think of the equation as a balanced scale.
Transposition
Transposition is a short form of applying inverse operations. Addition changes to subtraction, multiplication to division, and so on because the same inverse operation is being applied to both sides.
Variables on both sides
First simplify both sides. Move variable terms to one side and constants to the other. Then divide by the coefficient of the variable.
Brackets and fractions
Use the distributive property to remove brackets. For fractional equations, multiplying the complete equation by a common multiple of denominators often removes fractions and reduces errors.
Word problems
Choose a variable, translate the statement into an equation, solve, then interpret the answer with its unit or meaning.
Worked Examples
Subtract 5, then divide by 3.
Collect x-terms on one side.
Subtract 2, then multiply by 3.
Exam Traps
Quick Revision
Quick Revision
- A linear equation in one variable has one variable with highest power 1.
- Equality must be preserved by performing equivalent operations on both sides.
- Collect variable terms on one side and constants on the other.
- Remove brackets carefully and clear fractions when helpful.
- Always check the final value in the original equation.
Compact Practice
Solve x + 7 = 12.
View Solution
x = 5
Solve 4x = 28.
View Solution
x = 7
Solve 7x - 5 = 4x + 16.
View Solution
x = 7
Solve 3(x+2)=21.
View Solution
x = 5
A number doubled and increased by 3 gives 19. Find it.
View Solution
8
Final Chapter Summary
Chapter Summary
- A linear equation in one variable has one variable with highest power 1.
- Equality must be preserved by performing equivalent operations on both sides.
- Collect variable terms on one side and constants on the other.
- Remove brackets carefully and clear fractions when helpful.
- Always check the final value in the original equation.
- Prioritise correct method, clean working and final units where applicable.