Example 1
Write an equation for: 6 added to a number x gives 19.
- Start with the unknown variable x.
- Add 6 to x to get the expression x + 6.
- Set the expression equal to 19.
Answer: x + 6 = 19
📗 Class 7 maths · session 4 of 12 · 60 minutes · 🎁 free with an account
Simple equations
Welcome to the superhero maths lab! Captain Calc needs your help to unlock secret codes by solving simple equations.
🤖 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.
- Warm-up3 min
- Warm-up games5 min
- Understanding Equations and Building Them8 min
- Solving Equations Using Addition and Subtraction7 min
- Solving Equations with Multiplication and Division7 min
- Solving Real-Life Word Problems7 min
- Captain Calc's Vault Decoder6 min
- Market Mystery Solver5 min
- Shape & Perimeter Challenge6 min
- Quiz5 min
- Set the project1 min
By the end you can
- Identify variables, constants, and terms in a simple equation
- Convert word statements into simple algebraic equations
- Solve one-step and two-step equations using balancing methods
- Apply simple equations to solve real-life word problems
Before you start
- Basic operations with integers and positive numbers
- Understanding algebraic variables like x and y
Have ready
- Notebook and pencil
- Ruler for drawing balance scales
Class 7 · CBSE, ICSE and state boards
Warm-up · think first
Captain Calc places 3 secret boxes of equal weight and two 1 kg weights on one side of a balance scale. The other side has an 11 kg weight. The scale is perfectly balanced. How heavy is one secret box?
Show the answer
3 kg. Subtract 2 kg from both sides to get 3 boxes = 9 kg. Divide 9 by 3 to get 3 kg per box.
Teacher tip: Ask students to describe what happens when you remove equal weights from both sides of a scale.
🎮 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 mathematical expressions does not belong with the others? (x + 5 = 12 · 3y - 4 = 11 · 2a + 7 · m/2 = 9)
Answer: 2a + 7 does not belong because it is an expression without an equals sign. The other three are equations. - Would you rather solve an equation by subtracting 15 from both sides or by dividing both sides by 5? (Subtract 15 from both sides · Divide both sides by 5)
Answer: Both methods are great depending on the equation! Subtraction undoes addition, while division undoes multiplication. - An equation remains true if you add the exact same number to both sides. (Always · Sometimes · Never)
Answer: Always. Adding the same number to both sides keeps the equation perfectly balanced. - I am thinking of a number. If you multiply my number by 4 and add 6, you get 30. What is my number?
Answer: 6. Set up 4x + 6 = 30. Subtract 6 to get 4x = 24. Divide by 4 to get x = 6. - Why is an equation like a seesaw at the playground?
Answer: A seesaw stays level only when both sides carry equal weight. If you add or remove weight on one side, you must do the exact same on the other side to keep it balanced.
Part 1 of 4 · learn, see, practise
Understanding Equations and Building Them
An equation is a statement that two mathematical expressions are equal.
It always has an equals sign between the left hand side and right hand side.
Letters like x or y represent unknown values called variables.
Example 2
Write an equation for: 4 times a number y minus 3 is equal to 25.
- Multiply y by 4 to get 4y.
- Subtract 3 from 4y to get 4y - 3.
- Set the result equal to 25.
Answer: 4y - 3 = 25
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Stretch 🔥
Answers (for the teacher)
- p + 8 = 20
- m - 5 = 11
- 7z = 56
- k/4 = 9
- 2n + 3 = 17
- 5y - 7 = 28
🎁 Free for a year
Make a free account to open the rest of this lesson
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Unlocking the rest of this lesson gives you:
- Part 2: Solving Equations Using Addition and Subtraction, with practice at three levels
- Part 3: Solving Equations with Multiplication and Division, with practice at three levels
- Part 4: Solving Real-Life Word Problems, with practice at three levels
- Class activity 1: Captain Calc's Vault Decoder
- Class activity 2: Market Mystery Solver
- Class activity 3: Shape & Perimeter Challenge
- A 10-question quiz
- After-class project: Captain Calc's Equation Balance Mission
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
It takes a minute. Anyone under 13 signs up with a parent. The first 2 lessons of every course, every game and all maths practice stay free.
FAQ
Simple equations: questions
What is the difference between an algebraic expression and an equation?
An algebraic expression combines numbers and variables using operations like 2x + 5. An equation states that two expressions are equal using an equals sign, like 2x + 5 = 15.
Why must we do the same operation on both sides of an equation?
An equation represents perfect balance. Performing an operation on only one side breaks the equality, making the equation untrue.
How can I check if my answer to an equation is correct?
Substitute your answer back into the original equation in place of the variable. If both sides give the same final number, your solution is correct!
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