What is Solving Linear Equations in One Variable?

S3-SA1-0273

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Solving a linear equation in one variable means finding the value of the unknown letter (variable) that makes the equation true. An equation is like a balanced weighing scale, and we need to find the number that keeps it balanced.

Simple Example

Quick Example

Imagine you have some delicious ladoos (let's say 'x' ladoos) and your friend gives you 3 more. Now you have a total of 10 ladoos. The equation is x + 3 = 10. Solving it means finding how many ladoos you had initially.

Worked Example

Step-by-Step

Let's solve the equation: 2x + 5 = 15

Step 1: Our goal is to get 'x' by itself on one side. First, we need to move the '+ 5' to the other side. To do this, we subtract 5 from both sides of the equation to keep it balanced.
2x + 5 - 5 = 15 - 5

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Step 2: Simplify both sides.
2x = 10

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Step 3: Now, 'x' is being multiplied by 2. To get 'x' alone, we need to do the opposite operation, which is division. Divide both sides by 2.
2x / 2 = 10 / 2

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Step 4: Simplify to find the value of x.
x = 5

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Answer: The solution is x = 5.

Why It Matters

Solving equations is super important! It's like a superpower for problem-solving in many fields. Engineers use it to design bridges, data scientists use it to understand trends, and even game developers use it to make characters move realistically. It's a foundational skill for future careers in AI, Physics, and Computer Science.

Common Mistakes

MISTAKE: Adding a number to one side but subtracting it from the other. For example, in x + 5 = 10, changing it to x = 10 - 5 + 5. | CORRECTION: Whatever operation you do to one side of the equation, you must do the exact same operation to the other side to keep it balanced. If you subtract 5 from the left, subtract 5 from the right.

MISTAKE: Forgetting to change the sign when moving a term across the equals sign. For example, in 2x - 3 = 7, writing 2x = 7 - 3. | CORRECTION: When you move a term from one side of the equation to the other, you must change its sign (plus becomes minus, minus becomes plus). So, 2x - 3 = 7 becomes 2x = 7 + 3.

MISTAKE: Confusing multiplication with addition when isolating the variable. For example, in 3x = 12, subtracting 3 from both sides (3x - 3 = 12 - 3). | CORRECTION: If the variable is being multiplied by a number, you must divide both sides by that number. If it's being added/subtracted, you add/subtract. So, for 3x = 12, you divide by 3: x = 12 / 3.

Practice Questions

Try It Yourself

QUESTION: Solve for y: y + 7 = 12 | ANSWER: y = 5

QUESTION: Solve for p: 3p - 4 = 11 | ANSWER: p = 5

QUESTION: If a shopkeeper sells 'x' number of pens at Rs. 5 each and earns Rs. 40, what is the value of x? (Hint: Form an equation) | ANSWER: x = 8

MCQ

Quick Quiz

Which of the following is the correct solution for the equation x - 8 = 2?

x = 6

x = 10

x = -6

x = -10

The Correct Answer Is:

To solve x - 8 = 2, you need to add 8 to both sides of the equation. So, x - 8 + 8 = 2 + 8, which means x = 10. Options A, C, and D are incorrect because they do not correctly balance the equation.

Real World Connection

In the Real World

Think about planning a road trip! If you know the total distance you need to travel (say, Delhi to Jaipur, 280 km) and how many kilometers you've already covered (say, 100 km), you can use a linear equation (100 + x = 280) to find out how many more kilometers (x) you still need to drive. This helps in real-time navigation apps and logistics for delivery services like Zepto.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, like 2x + 5 = 15 | VARIABLE: An unknown quantity represented by a letter, usually x, y, or z | SOLVE: To find the value of the variable that makes the equation true | TERM: A single number or a variable, or numbers and variables multiplied together, like '2x' or '5'

What's Next

What to Learn Next

Great job understanding how to solve linear equations in one variable! Next, you can explore 'Solving Linear Equations with Variables on Both Sides'. This builds on what you've learned and will help you tackle even more interesting problems.