What is a Solution of an Equation?

S3-SA1-0015

Grade Level:

Class 6

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

Definition

What is it?

A solution of an equation is the value (or values) that makes the equation true. It's like finding the missing piece of a puzzle that balances both sides of the equation perfectly.

Simple Example

Quick Example

Imagine you have a box of ladoos, and your friend gives you 3 more. Now you have 10 ladoos in total. If 'x' is the number of ladoos you started with, the equation is x + 3 = 10. The solution is x = 7, because 7 + 3 = 10, which makes the statement true.

Worked Example

Step-by-Step

Let's find the solution for the equation: y - 5 = 8
---Step 1: We want to get 'y' by itself on one side of the equation. To do this, we need to remove the '- 5'.
---Step 2: The opposite of subtracting 5 is adding 5. So, we add 5 to BOTH sides of the equation to keep it balanced.
---Step 3: y - 5 + 5 = 8 + 5
---Step 4: This simplifies to y + 0 = 13
---Step 5: So, y = 13
---Step 6: To check our answer, substitute y = 13 back into the original equation: 13 - 5 = 8. Since 8 = 8, our solution is correct.
Answer: The solution is y = 13.

Why It Matters

Understanding solutions helps us solve real-world problems in many fields! Engineers use equations to design bridges, economists use them to predict market trends, and even game developers use them to program character movements. It's a foundational skill for future innovators!

Common Mistakes

MISTAKE: Only performing an operation on one side of the equation. For example, adding 2 to the left side but not the right side. | CORRECTION: Always perform the same operation (add, subtract, multiply, divide) on BOTH sides of the equation to keep it balanced.

MISTAKE: Confusing addition with subtraction or multiplication with division when trying to isolate the variable. For example, trying to subtract a number that is being multiplied. | CORRECTION: To undo an operation, always use its inverse operation. Add to undo subtraction, subtract to undo addition, multiply to undo division, and divide to undo multiplication.

MISTAKE: Not checking the answer by substituting it back into the original equation. | CORRECTION: Always substitute your found solution back into the original equation to verify that both sides are equal. This confirms your answer is correct.

Practice Questions

Try It Yourself

QUESTION: What is the solution for x + 4 = 12? | ANSWER: x = 8

QUESTION: Find the solution for 3 * m = 21. | ANSWER: m = 7

QUESTION: If you have 'p' rupees and spend 15 rupees on a chai, you are left with 35 rupees. Write an equation and find the solution for 'p'. | ANSWER: Equation: p - 15 = 35. Solution: p = 50

MCQ

Quick Quiz

Which value of 'k' is a solution to the equation k - 7 = 10?

k = 3

k = 7

k = 10

k = 17

The Correct Answer Is:

If k = 17, then 17 - 7 = 10, which makes the equation true. Options A, B, and C do not satisfy the equation.

Real World Connection

In the Real World

When you buy groceries, the shopkeeper calculates the total bill using equations. If you buy items worth 150 rupees and pay with a 200 rupee note, the equation is 150 + change = 200. Finding the 'change' is finding the solution! Similarly, apps like Zomato use solutions to calculate your total food bill and delivery charges.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign. | VARIABLE: A letter (like x, y, a) used to represent an unknown number. | EXPRESSION: A combination of numbers, variables, and operations (like x + 5 or 3y). | SOLVE: To find the value(s) of the variable that make the equation true. | INVERSE OPERATION: An operation that undoes another (e.g., addition is the inverse of subtraction).

What's Next

What to Learn Next

Great job understanding what a solution is! Next, you can explore how to solve more complex equations with variables on both sides, or equations involving multiplication and division. This will build your problem-solving skills even further!