Linear Equations in One Variable — Lesson
1) Hook — A Fun Real-Life Story to Grab Attention
Imagine you are at a cricket match between India and Australia. You buy some packets of chips and a bottle of soda for ₹150. The chips cost ₹30 per packet, and the soda costs ₹60. But you forget how many packets you bought! Can you figure out how many packets of chips you bought if the total is ₹150?
This kind of problem can be solved using linear equations in one variable. Let's dive in to learn how!
2) Core Concepts — What are Linear Equations in One Variable?
A linear equation in one variable is an equation that involves only one variable (like x) and has no exponents other than 1. It looks like this:
Our goal is to find the value of x that makes the equation true.
Example 1:
Solve: 3x + 9 = 0
| Step | Action | Result |
| 1 | Subtract 9 from both sides | 3x = -9 |
| 2 | Divide both sides by 3 | x = -3 |
Answer: x = -3
Example 2 (Cricket-themed):
During a cricket match, a batsman scored x runs in the first innings and 30 runs in the second innings. His total runs were 100. Find the runs scored in the first innings.
Equation: x + 30 = 100
Solution:
- Subtract 30 from both sides: x = 100 - 30
- x = 70
Answer: The batsman scored 70 runs in the first innings.
3) Key Formulas / Rules
Rule 1: To solve ax + b = 0, isolate x by:
x = -b / a
Rule 2: Whatever you do to one side of the equation, do the same to the other side.
Rule 3: Use inverse operations to isolate the variable (addition ↔ subtraction, multiplication ↔ division).
Summary Table: Solving Linear Equations
| Step | Operation | Example |
|---|---|---|
| 1 | Remove constant term by addition or subtraction | 3x + 9 = 0 → 3x = -9 |
| 2 | Divide by coefficient of variable | 3x = -9 → x = -9/3 = -3 |
4) Did You Know?
Linear equations have been used for thousands of years! Ancient Indian mathematicians like Bhaskara II solved linear and quadratic equations as early as the 12th century. So next time you solve an equation, remember you are following in the footsteps of brilliant minds from our own history!
5) Exam Tips — Common Mistakes & Board Patterns
- Always perform the same operation on both sides. Forgetting this leads to wrong answers.
- Watch out for signs (+/-). For example, subtracting a negative number is like adding.
- Check your answerx back into the original equation.
- Board exam pattern: Usually, you get 2–3 questions on linear equations, including word problems (like shopping bills or cricket scores).
- Practice word problems: Translate sentences into equations carefully before solving.
Remember: Practice makes perfect! Try solving these equations daily, and soon you’ll be a linear equation champion — just like your favourite cricket star hitting sixes!
Linear Equations in One Variable — Mcq
Linear Equations in One Variable — Mnemonic
Mnemonic 1: "BALANCED EQUATION" ⚖️
Remember: BALANCE your equation like a cricket match score!
- Bring all variables to one side (like bringing all your batsmen together 🏏)
- Add or subtract constants on the other side (like adjusting runs needed)
- Look for coefficients (players’ scores) and divide to find the variable’s value
- Always keep the equation balanced, just like a fair umpire’s call
- Never forget to check your solution by substituting back (like re-watching a Bollywood scene 🎬 to catch details)
- Calculate carefully and clearly
- Equate both sides perfectly for the final answer
Mnemonic 2: Hindi Rhyming Phrase 🎶
"Variable ko ek taraf lao,
Constants ko doosri taraf chalao,
Coefficient se divide karo,
Solution turant mil jao!"
Translation: Bring the variable to one side,
Move constants to the other side,
Divide by the coefficient,
And get the solution immediately!
Mnemonic 3: Funny Acronym "X=FUN" 😄
- Find the variable’s side first (x side)
- Use addition or subtraction to simplify
- Now divide by the coefficient to get x
Because solving linear equations should always be FUN!
Mission: Master This Topic!
Reinforce what you learned with fun activities
Ready to Battle? Test Your Knowledge!
Practice MCQs, build combos, climb the leaderboard!
Start Practice