NCERT Class 8 Mathematics Mathematics: Chapter 2 — Linear Equations in One Variable
This chapter, "Linear Equations in One Variable," from NCERT Class 8 Mathematics, revises algebraic expressions and equations. It defines linear equations as those with a highest variable power of 1 and only one variable. The chapter explains that an equation involves an equality sign (=) with a Left Hand Side (LHS) and Right Hand Side (RHS). Solutions are values of the variable that make LHS equal to RHS. It introduces methods to solve equations by performing identical operations on both sides to maintain balance. The text also begins to cover solving equations with variables on both sides, demonstrating techniques like transposing variables and clearing fractions by multiplying both sides by a common denominator. This foundational chapter prepares students for more complex algebraic problem-solving in mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 2 — Linear Equations in One Variable |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 433 |
Learning outcomes
- Understand the definition and properties of linear equations in one variable.
- Differentiate between algebraic expressions and equations.
- Identify the Left Hand Side (LHS) and Right Hand Side (RHS) of an equation.
- Solve linear equations with variables on one or both sides.
- Apply the concept of balancing equations through mathematical operations.
Vocabulary
| Word | Meaning |
|---|---|
| Algebraic expression | A combination of variables, constants, and mathematical operations. |
| Equation | A statement that asserts the equality of two expressions, involving an equality sign (=). |
| Variable | A symbol (usually a letter) that represents an unknown quantity. |
| Linear expression | An algebraic expression where the highest power of the variable is 1. |
| Linear equation in one variable | An equation involving only one variable, with the highest power of the variable being 1. |
| Solution | A value of the variable that makes an equation true. |
| LHS (Left Hand Side) | The expression on the left side of the equality sign in an equation. |
| RHS (Right Hand Side) | The expression on the right side of the equality sign in an equation. |
| Transposing | Moving a term from one side of an equation to the other, changing its sign. |
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Practice questions
- What is the highest power of the variable in a linear expression? Answer: The highest power of the variable is 1.
- What is the difference between an expression and an equation? Answer: An equation uses an equality sign (=) to state that two expressions are equal, while an expression does not.
- If 3x + 5 = 14, what is the value of x? Answer: Subtract 5 from both sides: 3x = 9. Divide by 3: x = 3.
- Solve the equation: 2y - 1 = y + 3 Answer: Subtract y from both sides: y - 1 = 3. Add 1 to both sides: y = 4.
Frequently asked questions
What is a linear equation in one variable?
It is an equation with only one variable, and the highest power of that variable is 1.
What does it mean to solve an equation?
Solving an equation means finding the value(s) of the variable that make the equation true (LHS = RHS).
How do you solve an equation like 2x - 3 = x + 2?
You can solve it by performing the same operation on both sides to isolate the variable, for example, by subtracting 'x' from both sides and then adding '3' to both sides.
What is the role of the equality sign in an equation?
The equality sign (=) indicates that the expression on the Left Hand Side (LHS) has the same value as the expression on the Right Hand Side (RHS).
Can we have variables on both sides of an equation?
Yes, equations can have expressions with variables on both the LHS and RHS, such as 2x - 3 = x + 2.
Related resources
Important topics
Topics covered
NCERT Class 8 Mathematics — Mathematics — Chapter 2 — Linear Equations in One Variable. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.