Linear Equations in 1 Variable Class 8: NCERT Concepts & Practice

Mathematics becomes more interesting when we start solving real-life problems using equations. One of the most important topics introduced in middle school is Linear Equations in One Variable. If you're a Class 8 student following the NCERT curriculum, this chapter builds a strong foundation for algebra and higher-level math.

In this blog, we’ll break down the NCERT Class 8 concepts of Linear Equations in One Variable in a simple and clear way. You’ll also find plenty of practice questions at the end to strengthen your understanding (no solutions included, so you can try them yourself!).

What is a Linear Equation in One Variable? (Class 8)

A linear equation in one variable is an equation that has only one variable and the highest power of that variable is 1.

Example:

• x + 5 = 9

• 2x - 3 = 7

• 5x = 20

Here, x is the variable, and the equation forms a straight line when plotted on a graph (that’s why it's called linear).

Important Terms You Should Know

Before solving equations, let’s understand some key terms from the NCERT Class 8 syllabus:

1. Variable

A symbol (usually a letter like x, y) that represents an unknown value.

2. Constant

A fixed number (like 2, 5, -3).

3. Equation

A mathematical statement with an equal sign (=).

4. Solution of an Equation

The value of the variable that satisfies the equation.

Standard Form of Linear Equation in One Variable

The general form is:

ax + b = 0

Where:

• a and b are constants

• x is the variable

• 

Solving Linear Equations in One Variable for Class 8

NCERT focuses on solving equations using basic operations. Let’s understand step-by-step.

1. Transposition Method

Move terms from one side to another by changing their signs.

Example:

x + 5 = 10
x = 10 - 5
x = 5

2. Using Basic Operations

We can add, subtract, multiply, or divide both sides of an equation to solve it.

Example:

2x = 12
x = 12 ÷ 2
x = 6

3. Simplifying Both Sides

Sometimes equations need simplification first.

Example:

2x + 3 = x + 7
2x - x = 7 - 3
x = 4

Equations with Variables on Both Sides

In Class 8 NCERT, you will often see equations where variables are on both sides.

Example:

3x + 2 = 2x + 5
3x - 2x = 5 - 2
x = 3

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Equations with Brackets

When brackets are involved, we first open the brackets using multiplication.

Example:

2(x + 3) = 10
2x + 6 = 10
2x = 4
x = 2

Equations with Fractions

These can look tricky but are easy when solved step-by-step.

Example:

x/2 + 3 = 7
x/2 = 4
x = 8

Real-Life Applications of Linear Equations (Class 8 Level)

NCERT also includes word problems to help you understand real-life usage.

Examples:

• Finding age

• Money transactions

• Number problems

• Perimeter and measurement

Example:

“The sum of a number and 5 is 15. Find the number.”

Let the number be x:
x + 5 = 15

Common Mistakes Students Should Avoid

• Not changing signs during transposition

• Forgetting to apply operations to both sides

• Making calculation errors

• Not simplifying expressions properly

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Methods to Solve Linear Equations in One Variable (Class 8)

In Class 8 NCERT, solving linear equations is all about maintaining balance. Whatever operation you perform on one side of the equation, you must do the same on the other side. This keeps the equation equal.

The most common method used is transposition, where numbers are moved from one side of the equation to the other by changing their signs. For example, a positive number becomes negative when moved to the other side, and vice versa.

Another important approach is simplification. If there are brackets or like terms, you first simplify both sides before solving. For instance, you may need to expand brackets using multiplication or combine like terms before isolating the variable.

You may also encounter equations where the variable is present on both sides. In such cases, bring all variable terms to one side and constant terms to the other side.

Practice Questions Example

1. x + 9 = 17

2. 2x = 14

3. 3x + 5 = 20

4. 4x - 7 = 9

5. 5x + 2 = 3x + 10

6. 7x - 3 = 5x + 9

7. 2(x + 4) = 18

8. 3(x - 2) = 12

Solving Linear Equations with Fractions and Brackets (Class 8)

In NCERT Class 8, equations may include fractions and brackets, which can seem difficult at first but become simple with step-by-step solving.

When fractions are involved, try to remove them by multiplying both sides by the LCM (Least Common Multiple) of the denominators. This helps convert the equation into a simpler form without fractions.

For equations with brackets, always remember to open the brackets first using multiplication. After that, combine like terms and solve as usual.

Being careful with signs and calculations is very important in this type of equation.

Practice Questions Example

1. x/2 + 4 = 10

2. x/3 - 2 = 5

3. (x/4) + 6 = 11

4. 2(x + 5) = 3x + 7

5. 4(x - 1) = 2x + 10

6. (2x)/5 = 6

7. x/2 + x/3 = 10

8. 3(x + 2) - 4 = 11

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Word Problems on Linear Equations in One Variable (Class 8)

Word problems are an important part of the NCERT Class 8 chapter because they help you apply equations in real-life situations. The key step is to convert the given statement into a mathematical equation.

Start by assuming the unknown number as a variable (like x). Then carefully translate the words into mathematical operations such as addition, subtraction, multiplication, or division. Once the equation is formed, solve it using the methods you’ve learned.

These problems often include situations like age, money, measurements, or numbers.

Practice Questions Example

1. The sum of a number and 12 is 25. Find the number.

2. A number is increased by 7 to get 19. What is the number?

3. The present age of a child is x. After 6 years, the age will be 20. Find x.

4. A number multiplied by 4 gives 28. Find the number.

5. The difference between a number and 9 is 11. Find the number.

6. The perimeter of a square is 36 cm. Find the length of one side.

7. A number when divided by 5 gives 6. Find the number.

8. The sum of two consecutive numbers is 21. Find the numbers.

Tips to Master Linear Equations (Class 8)

• Always solve step-by-step

• Keep equations balanced

• Practice daily

• Double-check your answer by substituting it back

Practice Questions: Linear Equations in One Variable Class 8

Try solving these questions on your own.

Section 1: Basic Linear Equations

1. x + 7 = 15

2. x - 9 = 3

3. 2x = 18

4. 5x = 25

5. x/3 = 6

Section 2: Equations with Variables on Both Sides

6. 2x + 5 = x + 9

7. 3x - 2 = x + 6

8. 5x + 3 = 3x + 11

9. 7x - 4 = 5x + 6

10. 4x + 2 = 2x + 10

Section 3: Equations with Brackets

11. 2(x + 4) = 16

12. 3(x - 2) = 9

13. 4(x + 1) = 20

14. 5(x - 3) = 10

15. 2(x + 5) = x + 11

Section 4: Equations with Fractions

16. x/2 + 3 = 9

17. x/4 - 2 = 3

18. (x/3) + 5 = 11

19. x/5 + 7 = 12

20. (2x)/3 = 8

Section 5: Word Problems (NCERT Level)

21. The sum of a number and 8 is 20. Find the number.

22. A number decreased by 5 gives 12. What is the number?

23. The present age of a person is x. After 5 years, the age will be 25. Find x.

24. The perimeter of a rectangle is 50 cm. If its length is 15 cm, find the width.

25. A number is multiplied by 3 and then increased by 6 to get 21. Find the number.

Section 6: Mixed Practice Questions

26. 3x + 7 = 2x + 15

27. 5(x + 2) = 3x + 16

28. 2(x - 3) + 4 = 10

29. x/2 + x/3 = 10

30. 4x - 5 = 3x + 9

Why This Chapter is Important

Understanding Linear Equations in One Variable (Class 8 NCERT) is essential because:

• It builds the base for algebra

• Helps in solving real-life problems

• Prepares you for higher classes (Class 9 & 10 math)

• Improves logical thinking

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Conclusion

Linear equations may seem confusing at first, but with regular practice and clear concepts, they become easy and fun to solve. Focus on understanding the steps rather than memorising them.

Start with simple problems and gradually move to complex ones. Practice consistently, and you’ll master this chapter in no time!

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