⚖️ Class 8 · Algebra

Linear Equations in One Variable for Class 8: notes, worked examples and practice

An equation is a balance. Whatever you do to one side you must do to the other, and that single idea solves every linear equation.

Updated 21 October 2026. Every worked example and answer on this page is checked by automated tests.

Try the practice questions WhatsApp a maths teacher

Notes

Linear Equations in One Variable: what you need to know

Chapter names and order differ by board and textbook edition, so follow your own textbook for the order.

What an equation is

An equation says two expressions are equal, such as 3x + 7 = 25. A solution is the value of the variable that makes it true. Here x = 6.

The balance method

Add, subtract, multiply or divide both sides by the same number (not zero). Do the same to every term, and the equation stays balanced.

Variables on both sides

Collect the variable terms on one side and the numbers on the other. In 5x − 4 = 2x + 11 subtract 2x from both sides to get 3x − 4 = 11, then add 4 and divide by 3.

Brackets and fractions

Expand brackets first. If there are fractions, multiply every term by the LCM of the denominators to clear them.

Word problems

Let a letter stand for the unknown, write an equation from the words, solve it and check the answer against the story.

Formulas and rules to remember

ax + b = c gives x = (c − b) ÷ a
Same operation on both sides keeps the equation balanced
Check: substitute x back into the original equation

Solved examples

Example 1

Solve 3x + 7 = 25.

Subtract 7 from both sides: 3x = 18.
Divide by 3: x = 6.

Answer: x = 6

Example 2

Solve 5x − 4 = 2x + 11.

Subtract 2x from both sides: 3x − 4 = 11.
Add 4: 3x = 15.
Divide by 3: x = 5.

Answer: x = 5

Example 3

Solve (x + 3) ÷ 2 = 7.

Multiply both sides by 2: x + 3 = 14.
Subtract 3: x = 11.

Answer: x = 11

Example 4

The sum of two consecutive numbers is 63. Find them.

Let the numbers be n and n + 1.
n + n + 1 = 63, so 2n = 62 and n = 31.
The numbers are 31 and 32.

Answer: 31 and 32

Avoid these

Common mistakes

Doing the operation on one term only

If you divide by 3, divide every term on both sides, not just one.

Sign errors when moving a term

Moving +4 to the other side makes it −4. Add or subtract on both sides rather than 'moving' it in your head.

Skipping the check

Substitute your answer into the original equation. If both sides match, it is right.

10 practice questions with answers

Try each question on paper first, then tap it to check your answer. The questions are generated by code and each answer is checked.

Solve 10x = 160. x =
Answer: 16
Solve x − 4 = 14. x =
Answer: 18
Solve x ÷ 11 = 19. x =
Answer: 209
Solve 2x + 17 = 25. x =
Answer: 4
Solve 9x − 6 = 21. x =
Answer: 3
Solve 3x + 2 = 5. x =
Answer: 1
Solve 9x − 16 = 29. x =
Answer: 5
Solve 2x + 2 = 10. x =
Answer: 4
Solve 9x − 6 = 120. x =
Answer: 14
Solve 7x + 11 = 25. x =
Answer: 2

More practice

Printable worksheets (PDF with answers)

One-step equations (Grade 6)
Two-step equations (Grade 7)

Games and lessons

Maths dictionary

FAQ

Linear Equations in One Variable Class 8: questions students ask

How do I solve a linear equation?

Use the balance method: do the same operation to both sides until the variable is alone.

What if the variable is on both sides?

Subtract the smaller variable term from both sides first so that the variable appears on one side only.

How do I check my answer?

Put the value back into the original equation. If the left and right sides are equal, the answer is correct.

How do I solve word problems with equations?

Let a letter stand for the unknown, write an equation from the sentence, solve it and check it against the story.

Which board is this linear equations in one variable page for?

It covers the ideas taught in CBSE, ICSE and state-board maths. Chapter names and order differ by board and textbook edition, so follow your own textbook for the exact order.

Need help with linear equations in one variable?

Tell us the class, board and what feels hard. We match a maths teacher from our network and confirm the format before anything is booked.

Tell us the learner’s age or grade and goals
We’ll suggest a suitable class or learning path
We’ll confirm format, timing and fees with a parent or guardian

Play it, don't just read it

Try it now: One-step equations

Eight quick questions with instant feedback. Your score is saved on this device and counts in the games and learning paths too.

All free games →

One-step equations (Grade 6): Solving equations such as x + 7 = 15 or 4x = 28. Open the practice page or print a worksheet.

Or play a game

Today's maths challengeFive questions · the same for everyone today · keep your streak goingPlay