Have you ever been in a situation where you’re trying to find an unknown number?
For example:
“I think of a number. I add 3 to it and get 10. What is the number?”
This is where linear equations help us!
Let’s learn what linear equations are, why we need them, and how to solve them — step by step.
Why Do We Need Linear Equations?
We face many problems in real life where we don’t know a value and need to find it.
Examples:
- How much money did I have before I spent some?
- How many chocolates were there before sharing them equally?
- What is the price of one pencil if 5 pencils cost ₹50?
Linear equations help us solve real-life problems like these.
What Is a Linear Equation?
A linear equation is a math sentence that shows two expressions are equal.
It has:
- One variable (like x or y)
- No powers (no x², x³, etc.)
- The highest power of the variable is 1
Example:
x + 3 = 10
This is a linear equation because:
- It has one variable (x)
- The power of x is 1
- It is in a straight-line format
What Problems Does a Linear Equation Solve?
It helps you:
- Find unknown numbers
- Solve word problems in maths
- Understand money, distance, and age problems
- Make tables and graphs
How to Solve a Linear Equation
Let’s take an example:
x + 5 = 12
We want to find the value of x.
Step-by-step:
- Subtract 5 from both sides to keep balance:
- x + 5 – 5 = 12 – 5
- Now solve:
- x = 7
That’s it! The unknown number is 7.
Another Example:
3x = 15
- Divide both sides by 3:
- 3x ÷ 3 = 15 ÷ 3
- Solve:
- x = 5
Common Mistakes to Avoid
- Always do the same operation on both sides
- Keep your equation balanced
- Don’t forget to check your answer by putting it back in the original equation
Glossary: Important Terms
| Term | Meaning |
| Variable | A letter (like x or y) that stands for an unknown number |
| Equation | A math sentence that says two things are equal (uses the = sign) |
| Linear | Means “straight line” – here, it means no powers or squares in the equation |
| Constant | A number whose value does not change |
| Coefficient | A number that is multiplied with a variable (In 3x, 3 is the coefficient) |
| Solve | To find the value of the variable |
| Operation | A math action: add (+), subtract (−), multiply (×), or divide (÷) |
Try This Yourself
- x + 4 = 9
- 2x = 12
- x – 5 = 3
- 5x + 2 = 17
Can you solve these? Check your answers by putting the value back in the equation!
Final Tip
Practice is the key. The more you solve, the easier it becomes.
If you understand how to balance a linear equation, it’s like solving a puzzle. Keep trying — you’ll get better every day!
Still if you need help in solving Linear Equations, try our Linear Equation Solver. Just hit the button!
