Linear Equations in One Variable — Lesson
1) Hook — A Fun Real-Life Example
Imagine you are at a local Indian sweet shop in Delhi. You want to buy some ladoos and barfis. Each ladoo costs ₹10 and each barfi costs ₹15. You have ₹100 in your pocket and want to buy a total of 8 sweets. How many ladoos and barfis can you buy? This real-life problem can be solved using linear equations in one variable, helping you decide the exact number of sweets you can afford!
2) Core Concepts — What are Linear Equations in One Variable?
A linear equation in one variable is an equation that can be written in the form:
where a and b are constants, and x is the variable. The highest power of x is 1.
Goal: Find the value of x that makes the equation true.
Example 1:
Solve the equation: 3x + 5 = 20
| 3x + 5 = 20 |
| 3x = 20 - 5 |
| 3x = 15 |
| x = 15 ÷ 3 = 5 |
Answer: x = 5
Example 2 (Word Problem):
Ravi has ₹500. He buys a book for ₹x and a pen for ₹(x + 50). If he spends all his money, find the cost of the book.
Equation: x + (x + 50) = 500
| 2x + 50 = 500 |
| 2x = 500 - 50 = 450 |
| x = 450 ÷ 2 = 225 |
Answer: The book costs ₹225.
3) Key Formulas / Rules
Rule 1: To solve ax + b = 0, isolate x:
x = -b / a
Rule 2: Perform the same operation on both sides of the equation.
Rule 3: Remove brackets and combine like terms before solving.
4) Did You Know?
The concept of solving equations dates back to ancient India! The famous mathematician Brahmagupta (7th century) wrote about solving linear and quadratic equations in his book Brahmasphutasiddhanta. So, when you solve linear equations, you are following a tradition thousands of years old!
5) Exam Tips — Common Mistakes & Board Exam Patterns
- Always simplify both sides before isolating the variable. Don’t forget to remove brackets carefully.
- Do not divide by zero. If the coefficient of x is zero, check if the equation has infinite or no solutions.
- Check your solution by substituting the value of x back into the original equation.
- Word problems: Carefully translate the problem into an equation. Define variables clearly.
- Board exam pattern: Questions usually ask to solve linear equations or apply them in word problems. Marks range from 2 to 4 per question.
- Mnemonic to remember solving steps: “Simplify, Isolate, Calculate, Verify” (SICV).
Linear Equations in One Variable — Mcq
Linear Equations in One Variable — Mnemonic
Mnemonic 1: "BALANCE" Rule for Solving Linear Equations ⚖️
- Bring variables to one side
- Add or subtract constants on both sides
- Lastly, divide or multiply to isolate the variable
- Always keep the equation balanced like a tarazu (scale) ⚖️
- Never forget to check your solution by substituting back
- Calculate carefully
- Ensure the variable’s coefficient is 1 at the end
Remember: BALANCE your equation just like your mom balances your diet! 🍎🥦
Mnemonic 2: Hindi Rhyming Trick for Equation Steps 🎶
“Variable ek taraf lao,
Number doosri taraf badhao,
Divide karo, multiply mat bhoolo,
Answer milega, tension mat lo!”
Translation: Bring variable to one side,
Move numbers to the other side,
Divide carefully, don’t forget multiply,
You’ll get the answer, no need to worry!
Mnemonic 3: Funny Acronym "S.I.D.E" for Quick Solving 🚀
- Simplify both sides
- Isolate the variable term
- Divide by the coefficient
- Evaluate and check answer
Think of it as “SIDE” because you always move terms to one side first! 😄
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