What is Solving an Equation? | Simple Explanation for Class 5

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What is Solving an Equation (Simple — Finding x)?

Grade Level:

Class 5

Maths, Computing, AI, Physics, Chemistry

Definition

What is it?

Solving an equation means finding the value of the unknown number (usually called 'x') that makes the equation true. Think of it like a puzzle where you need to figure out the missing piece to balance both sides.

Simple Example

Quick Example

Imagine you bought a cricket bat for Rs 500 and a ball, and the total bill was Rs 550. If we write this as an equation: 500 + x = 550. Solving this equation means finding the price of the ball (x).

Worked Example

Step-by-Step

Let's solve the equation: x + 7 = 15

1. Our goal is to get 'x' by itself on one side of the equals sign.
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2. To remove '+ 7' from the left side, we do the opposite operation: subtract 7.
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3. Remember, whatever you do to one side of the equation, you must do to the other side to keep it balanced. So, subtract 7 from both sides:
x + 7 - 7 = 15 - 7
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4. Simplify both sides:
x = 8
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5. To check our answer, substitute x = 8 back into the original equation:
8 + 7 = 15
15 = 15 (This is true, so our answer is correct).

Answer: x = 8

Why It Matters

Solving equations is a fundamental skill used everywhere! Scientists use it to calculate rocket trajectories for ISRO, engineers use it to design buildings, and even computer programmers use it to write code for apps. It's the basis for understanding how things work in physics, chemistry, and AI.

Common Mistakes

MISTAKE: Adding or subtracting only on one side of the equation | CORRECTION: Always perform the same operation (add, subtract, multiply, divide) on BOTH sides of the equals sign to keep the equation balanced.

MISTAKE: Confusing addition/subtraction with multiplication/division. For example, to undo 'x + 5', trying to divide by 5 | CORRECTION: To undo addition, subtract. To undo subtraction, add. To undo multiplication, divide. To undo division, multiply.

MISTAKE: Not simplifying correctly after an operation, like '10 - 3 = 6' | CORRECTION: Double-check your basic arithmetic after each step to avoid simple calculation errors.

Practice Questions

Try It Yourself

QUESTION: If you have x rupees and your friend gives you 20 rupees, you now have 75 rupees. How many rupees did you have initially? (x + 20 = 75) | ANSWER: x = 55

QUESTION: A auto-rickshaw driver covered a distance of 45 km today. This is 15 km less than what he covered yesterday. How much distance did he cover yesterday? (x - 15 = 45) | ANSWER: x = 60

QUESTION: You bought 3 packets of biscuits, and each packet costs the same. If the total bill was Rs 60, how much did one packet cost? (3 * x = 60) | ANSWER: x = 20

MCQ

Quick Quiz

Which operation should you do to solve 'x - 9 = 20'?

Subtract 9 from both sides

Add 9 to both sides

Multiply both sides by 9

Divide both sides by 9

The Correct Answer Is:

To isolate 'x' in 'x - 9 = 20', you need to undo the '- 9'. The opposite of subtracting 9 is adding 9. So, you add 9 to both sides of the equation.

Real World Connection

In the Real World

When you buy groceries, the shopkeeper might use a simple equation to figure out the change you need. Or, when a delivery app like Swiggy calculates the estimated delivery time, it uses equations to factor in distance, traffic, and speed to find the unknown time.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing that two expressions are equal, usually with an equals sign (=) | UNKNOWN: The letter (like 'x') representing the number we need to find | SOLVE: To find the value of the unknown that makes the equation true | BALANCE: Keeping both sides of the equation equal by doing the same operation to both sides

What's Next

What to Learn Next

Great job understanding how to solve simple equations! Next, you can learn about solving equations with multiplication and division, and then move on to equations with more steps or involving fractions. Each new concept builds on this basic skill!