What is No Solution?

S3-SA1-0030

Grade Level:

Class 6

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

Definition

What is it?

When we try to solve a math problem or equation, sometimes there is no value that makes the statement true. This means the problem has 'No Solution'. It's like asking for a number that is both bigger than 5 and smaller than 3 at the same time, which is impossible.

Simple Example

Quick Example

Imagine your cricket coach says, 'Score more than 100 runs AND less than 50 runs in today's match.' Can you do both? No, it's impossible! You can't score more than 100 and also less than 50 at the same time. This situation has 'No Solution'.

Worked Example

Step-by-Step

Let's try to solve this equation: x + 5 = x + 10

Step 1: We want to get 'x' by itself on one side of the equation.

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Step 2: Let's try to subtract 'x' from both sides of the equation.
x + 5 - x = x + 10 - x

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Step 3: Simplify both sides.
5 = 10

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Step 4: Look at the result. Is 5 equal to 10? No, it's not! This statement is false.

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Step 5: Since we reached a false statement (5 = 10) and 'x' disappeared, it means there is no value of 'x' that can make the original equation true.

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Answer: The equation has No Solution.

Why It Matters

Understanding 'No Solution' is crucial in many fields. Engineers use it to know when a design is impossible, like building a bridge that can't stand. In computer science, it helps programmers identify logical errors in code. Even economists use it to understand why certain market conditions can't exist, helping them make better predictions.

Common Mistakes

MISTAKE: Thinking that 'No Solution' means you made a mistake in solving the problem. | CORRECTION: 'No Solution' is a valid answer! It means the problem itself doesn't have a number that fits the conditions.

MISTAKE: Writing 'x = no solution' or 'solution = 0'. | CORRECTION: The correct way to state it is simply 'No Solution' or sometimes 'Empty Set'. Zero is a number, but 'No Solution' means no number works.

MISTAKE: Confusing 'No Solution' with 'Infinite Solutions'. | CORRECTION: 'No Solution' means NO number works. 'Infinite Solutions' means EVERY number works (e.g., x + 2 = x + 2, which simplifies to 2 = 2, a true statement).

Practice Questions

Try It Yourself

QUESTION: Does the equation 2x + 1 = 2x + 7 have a solution? | ANSWER: No Solution

QUESTION: A chaiwala says, 'I have some chai cups. If I add 3 cups, I'll have the same number of cups as if I started with the same amount and added 5 cups.' How many cups did he start with? | ANSWER: No Solution (This translates to x + 3 = x + 5)

QUESTION: Find the value of 'y' that satisfies both y > 10 and y < 5. | ANSWER: No Solution

MCQ

Quick Quiz

Which of the following equations has No Solution?

x + 3 = 7

2x = x + x

5 + x = x - 2

3x - x = 2x

The Correct Answer Is:

In option C, if you subtract 'x' from both sides, you get 5 = -2, which is a false statement. This means there is no value of 'x' that can make the equation true, so it has No Solution.

Real World Connection

In the Real World

Imagine you're booking an auto-rickshaw using an app like Ola or Uber. If you put your pickup location as 'Delhi' and your drop-off location as 'Mumbai', and then try to find an auto that can cover that distance in 5 minutes, the app will show 'No ride found' or 'No Solution'. This is because the conditions (distance and time) are impossible to meet simultaneously.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign. | SOLUTION: The value(s) that make an equation true. | VARIABLE: A letter (like x or y) representing an unknown number. | FALSE STATEMENT: A statement that is not true (e.g., 5 = 10).

What's Next

What to Learn Next

Now that you understand 'No Solution', you can explore equations that have 'One Solution' (the most common type) and 'Infinite Solutions'. This will give you a complete picture of all possible outcomes when solving equations, making you a math problem-solving champ!