📙 Class 8 maths · session 2 of 13 · 60 minutes · free

Linear equations in one variable

Greetings, Math Crusader! Captain Calc needs your analytical powers to solve secret code equations and save Math City.

🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.

A complete lesson · 60 minutes

Teach it, see it, practise it, all on this page.

Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.

See the teacher's plan

Warm-up3 min
Warm-up games5 min
Understanding Linear Equations in One Variable8 min
Variables on Both Sides7 min
Equations with Brackets and Fractions7 min
Solving Real-Life Word Problems7 min
The Villains' Vault6 min
Dual Variable Duel5 min
Word Problem Rescue6 min
Quiz5 min
Set the project1 min

By the end you can

Identify linear equations in one variable
Solve linear equations with variables on one side or both sides
Simplify equations containing brackets and fractional expressions
Form and solve linear equations from real-life word problems

Before you start

Basic algebraic expressions and terms
Four basic arithmetic operations on integers and fractions

Have ready

Notebook and pen
Ruler for drawing balance scales

Class 8 · CBSE, ICSE and state boards

Warm-up · think first

Captain Calc has a secret number. If you double it and add 6, you get 20. What is the secret number?

Show the answer

7. Because 2 × 7 = 14, and 14 + 6 = 20.

Teacher tip: Ask students how they worked backward from 20 to find the original number.

More warm-ups for every class →

🎮 Warm-up games · 5 quick games

Play with Captain Calc

Six minutes with Captain Calc. Vote, say why, then show the answer.

Which of these equations does not belong with the others? (2x + 5 = 11 · x² - 4 = 0 · 3y - 7 = 8 · 4z = 20)
Answer: x² - 4 = 0 does not belong because the power of x is 2, making it quadratic rather than linear.
Would you rather solve 5(x - 2) = 15 by expanding the brackets first or by dividing both sides by 5 first? (Expand brackets first: 5x - 10 = 15 · Divide by 5 first: x - 2 = 3)
Answer: Both methods give x = 5! Dividing by 5 first keeps the numbers smaller.
If you add the same number to both sides of an equation, the balance stays equal. (Always · Sometimes · Never)
Answer: Always. Adding equal quantities to equal quantities keeps both sides equal.
Rohan has ₹50 more than Ananya. Together they have ₹250. How much money does Ananya have?
Answer: ₹100. If Ananya has x, then Rohan has x + 50. Together x + x + 50 = 250, so 2x = 200 and x = 100.
Why do we call the equals sign '=' the center beam of a balance scale in algebra?
Answer: Because whatever change you make on one side, you must make on the other side to keep it balanced.

Part 1 of 4 · learn, see, practise

Understanding Linear Equations in One Variable

An algebraic equation is a statement showing two expressions are equal.

A linear equation in one variable contains only one unknown letter, and its highest power is 1.

To solve an equation, isolate the variable on one side using inverse operations.

Example 1

Solve for x: 3x - 7 = 14

Add 7 to both sides: 3x = 14 + 7
Simplify: 3x = 21
Divide both sides by 3: x = 7

Answer: x = 7

Example 2

Solve for y: y/4 + 5 = 9

Subtract 5 from both sides: y/4 = 4
Multiply both sides by 4: y = 16

Answer: y = 16

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up1Solve: x + 5 = 12

Warm-up2Solve: y - 8 = 3

Core3Solve: 3m = 21

Core4Solve: z / 4 = 6

Stretch 🔥5Solve: 2x + 7 = 19

Stretch 🔥6Solve: 5p - 3 = 22

Answers (for the teacher)

Part 2 of 4 · learn, see, practise

Variables on Both Sides

Sometimes the unknown variable appears on both the left and right sides of the equation.

Collect all terms containing the variable on one side using addition or subtraction.

Collect all constant numbers on the opposite side, then solve for the variable.

Example 1

Solve for x: 5x + 4 = 3x + 12

Subtract 3x from both sides: 2x + 4 = 12
Subtract 4 from both sides: 2x = 8
Divide both sides by 2: x = 4

Answer: x = 4

Example 2

Solve for n: 7n - 5 = 2n + 15

Subtract 2n from both sides: 5n - 5 = 15
Add 5 to both sides: 5n = 20
Divide both sides by 5: n = 4

Answer: n = 4

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up1Solve: 4x = 2x + 10

Warm-up2Solve: 5y - 6 = 2y + 9

Core3Solve: 7n + 2 = 3n + 18

Core4Solve: 6k - 5 = 2k + 11

Stretch 🔥5Solve: 8t - 14 = 3t + 21

Stretch 🔥6Solve: 9x - 12 = 4x + 13

Answers (for the teacher)

Part 3 of 4 · learn, see, practise

Equations with Brackets and Fractions

When an equation has brackets, use the distributive property to expand them first.

If fractions are present, multiply the entire equation by the common denominator to clear them.

Simplify each side step by step until you can isolate the variable.

Example 1

Solve for x: 3(x - 2) = 15

Expand brackets: 3x - 6 = 15
Add 6 to both sides: 3x = 21
Divide by 3: x = 7

Answer: x = 7

Example 2

Solve for m: (m + 2)/3 = 5

Multiply both sides by 3: m + 2 = 15
Subtract 2 from both sides: m = 13

Answer: m = 13

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up1Solve: 3(x + 2) = 21

Warm-up2Solve: 4(y - 3) = 16

Core3Solve: x/3 + 4 = 9

Core4Solve: m/2 - 3 = 5

Stretch 🔥5Solve: 2(3p - 1) = 28

Stretch 🔥6Solve: (x + 1)/2 = 5

Answers (for the teacher)

Part 4 of 4 · learn, see, practise

Solving Real-Life Word Problems

Read the problem carefully and choose a variable letter for the unknown quantity.

Translate the words into an algebraic equation using mathematical operations.

Solve the equation and state the final answer clearly with appropriate context.

Example 1

The sum of two consecutive numbers is 31. Find the smaller number.

Let the smaller number be x. The next number is x + 1.
Write equation: x + (x + 1) = 31
Combine terms: 2x + 1 = 31
Subtract 1: 2x = 30, so x = 15

Answer: 15

Example 2

The perimeter of a rectangle is 36 cm. Length is 2 cm more than width. Find width in cm.

Let width be w. Length = w + 2.
Perimeter formula: 2(length + width) = 36
Write equation: 2(w + 2 + w) = 36
Simplify: 2(2w + 2) = 36 -> 4w + 4 = 36
Subtract 4: 4w = 32, so w = 8

Answer: 8

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up1The sum of two numbers is 25. One number is 5 more than the other. Find the smaller number.

Warm-up2Priya is 4 years older than Aman. The sum of their ages is 24. Find Aman's age in years.

Core3The perimeter of a rectangle is 40 cm. Length is 4 cm more than width. Find width in cm.

Core4Three consecutive integers add up to 45. Find the smallest integer.

Stretch 🔥5Aarav has ₹5 coins and ₹10 coins. Total 15 coins worth ₹110. How many ₹10 coins does he have?

Stretch 🔥6A number multiplied by 4 and increased by 7 gives 31. Find the number.

Answers (for the teacher)

Watch out

Common mistakes

Forgetting to change the sign of a term when moving it across the equals sign.

Remember that moving a term to the opposite side flips positive to negative and vice versa.

Multiplying only the first term inside brackets instead of all terms.

Use the distributive property: multiply the outside number by every term inside brackets.

Dividing only one term by a number when clearing a coefficient.

Always divide every term on both sides by the same non-zero number.

Class activity 1 of 3

The Villains' Vault

Crack the secret codes to unlock Captain Calc's hidden vault!

Solve each linear equation on your scratchpad.
Check your answer by plugging it back into the original equation.
Type your single numerical answer into the vault computer.

1Solve: 2x = 18

2Solve: y - 7 = 14

3Solve: 3m + 5 = 26

4Solve: 4k - 9 = 15

5Solve: p / 5 = 8

Answers (for the teacher)

Class activity 2 of 3

Dual Variable Duel

Villains are attacking from both sides! Balance the equations to defeat them.

Move all variable terms to the left side.
Move all constant terms to the right side.
Divide to find the value of the variable.

1Solve: 5x = 2x + 12

2Solve: 7y - 4 = 3y + 16

3Solve: 8n + 3 = 5n + 18

4Solve: 10k - 15 = 4k + 9

5Solve: 6w + 2 = 2w + 26

Answers (for the teacher)

Class activity 3 of 3

Word Problem Rescue

Help citizens of Math City convert their story problems into algebra!

Identify the unknown variable.
Set up the correct linear equation.
Solve for the unknown value.

1The sum of two numbers is 30. One is 6 more than the other. Find the smaller number.

2Perimeter of a square is 48 cm. Find side length in cm.

3Rohan is 5 years older than Maya. Total age is 29. Find Maya's age in years.

4A number divided by 4 plus 3 equals 9. Find the number.

5Three consecutive integers sum to 36. Find the middle integer.

Answers (for the teacher)

After class · project

Captain Calc's Equation Creator

Design your own comic-style story problem and convert it into a linear equation with step-by-step solutions.

Think of a superhero scenario involving unknown values like currency, age, or distance.
Write down the word problem clearly.
Define the unknown variable and formulate the equation.
Solve the equation step by step and present your work clearly.

What to make: A single poster or written report featuring your comic word problem, equation, and solution.

Stretch: Create a problem with variables on both sides and fractional coefficients!

How it is marked

Look for	Done well when
Clarity of Story Problem	The story is engaging, clear, and sets up a valid single-variable relationship.
Equation Setup	The linear equation correctly translates the story details.
Mathematical Accuracy	Every step of the solution is correct with no algebraic errors.
Presentation	Work is neat, organized, and styled like a comic comic strip.

Project template

Copy it onto paper or print the practice sheet.

Superhero Story Title: _____
Word Problem Scenario: _____
Let the variable x represent: _____
Formulated Equation: _____
Step-by-Step Solution: _____
Final Answer with Units: _____

Homework

Practise at home

Try each on paper, then tap to see the answer and working. Or print the practice sheet.

Solve: 3x + 8 = 23
x = 5. Working: 3x = 15, x = 15/3 = 5.
Solve: 7y - 5 = 4y + 10
y = 5. Working: 3y = 15, y = 15/3 = 5.
Solve: 4(m - 2) = 20
m = 7. Working: 4m - 8 = 20, 4m = 28, m = 7.
Solve: (x + 3)/4 = 5
x = 17. Working: x + 3 = 20, x = 20 - 3 = 17.
The length of a rectangle is 3 cm more than its width. Its perimeter is 34 cm. Find its width in cm.
7 cm. Working: 2(w + w + 3) = 34, 4w + 6 = 34, 4w = 28, w = 7.
The sum of three consecutive numbers is 51. Find the largest number.
18. Working: x + x+1 + x+2 = 51, 3x + 3 = 51, 3x = 48, x = 16, largest is 18.

🔥 Challenge round · finished early?

The hardest questions of the lesson, no notes

Cover the notes and try these from memory. They are meant to make you think hard: draw, try small cases, and check your answer.

Stretch 🔥1Solve: 2x + 7 = 19

Stretch 🔥2Solve: 5p - 3 = 22

Stretch 🔥3Solve: 8t - 14 = 3t + 21

Stretch 🔥4Solve: 9x - 12 = 4x + 13

Stretch 🔥5Solve: 2(3p - 1) = 28

Stretch 🔥6Solve: (x + 1)/2 = 5

Stretch 🔥7Aarav has ₹5 coins and ₹10 coins. Total 15 coins worth ₹110. How many ₹10 coins does he have?

Stretch 🔥8A number multiplied by 4 and increased by 7 gives 31. Find the number.

Answers (for the teacher)

🧠 Think-hard question

Solve for x: (2x + 3)/5 - (x - 2)/3 = 2. Show each step clearly.

Talk it through or use the drawing board. There is more than one way to get there.

🎯 Practice mode: one question at a time 🧩 Brain warm-ups 🎮 Maths and logic games

Quiz · 10 questions

Final quiz: check what you learned

Pick an answer to see if it is right and why. Your best score is saved on this device.

1Which of these is a linear equation in one variable?

Show the answer

4x - 5 = 11. It has only one variable x, and its power is 1.

2Solve for x: 3x = 18

Show the answer

6. Dividing both sides by 3 gives x = 6.

3Solve for y: y/4 = 7

Show the answer

28. Multiplying both sides by 4 gives y = 28.

4Solve for x: 2x + 5 = 17

Show the answer

6. Subtracting 5 gives 2x = 12, so x = 6.

5Solve for m: 5m - 4 = 2m + 11

Show the answer

5. Subtracting 2m gives 3m - 4 = 11, adding 4 gives 3m = 15, so m = 5.

6Solve for x: 3(x - 4) = 15

Show the answer

9. Expanding gives 3x - 12 = 15, adding 12 gives 3x = 27, so x = 9.

7If 4 is subtracted from a number, the result is 12. What is the number?

Show the answer

16. The equation is n - 4 = 12, so n = 16.

8Solve for x: 2x / 3 = 8

Show the answer

12. Multiplying by 3 gives 2x = 24, dividing by 2 gives x = 12.

9The perimeter of a rectangle is 30 cm. Its length is 8 cm. What is its width in cm?

Show the answer

7. 2(8 + w) = 30 gives 16 + 2w = 30, so 2w = 14 and w = 7.

10Three consecutive integers add up to 27. What is the smallest integer?

Show the answer

8. x + (x+1) + (x+2) = 27 gives 3x + 3 = 27, so 3x = 24 and x = 8.

For parents and teachers

The 60-minute lesson plan

Use it as it is, or stretch any part over two sessions. Each row links to the part of the page you need.

Time	Part	The teacher	The learner
0–3 min	Warm-up	Ask the question and wait for a guess before any hint.	Guess, then explain.
3–8 min	Warm-up games	Play three or four games. Ask for a reason each time.	Vote and say why.
8–16 min	Understanding Linear Equations in One Variable	Explain, then reveal the examples one step at a time.	Practise up to the stretch question.
16–23 min	Variables on Both Sides	Explain, then show the examples.	Practise.
23–30 min	Equations with Brackets and Fractions	Explain, then show the examples.	Practise.
30–37 min	Solving Real-Life Word Problems	Explain, then show the examples.	Practise; the stretch can be homework.
37–43 min	The Villains' Vault	Let learners work alone; hint only after a wrong check.	Solve and check.
43–48 min	Dual Variable Duel	Do the first item together.	Finish the activity.
48–54 min	Word Problem Rescue	Set as homework if time is short.	Solve the mission.
54–59 min	Quiz	Read each question aloud; vote, then check.	Answer and read why.
59–60 min	Set the project	Show the template and agree a due date.	Start the project.

Questions to ask

What is the first step you take when a variable appears on both sides of the equals sign?
How can you check if your final numerical answer is correct without asking a teacher?
Why must we perform the exact same operation on both sides of an equation?

If it feels hard

If a student struggles, use physical counters or draw a balance scale. Place mystery boxes for variables and counters for numbers, demonstrating that removing or adding items to one side requires doing the exact same to the other side.

If it feels easy

Solve for x: (2x + 3)/5 - (x - 2)/3 = 2. Show each step clearly.

FAQ