What is a True Inequality?

S1-SA5-0185

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

A true inequality is a mathematical statement that compares two values or expressions and shows that one is not equal to the other. It uses symbols like '>' (greater than), '<' (less than), '>=' (greater than or equal to), or '<=' (less than or equal to) to show this difference. When an inequality is true, it means the comparison it makes is correct.

Simple Example

Quick Example

Imagine your friend scored 85 runs in a cricket match, and you scored 70 runs. We can write this as an inequality: 85 > 70. This is a true inequality because 85 is indeed greater than 70. It correctly shows that your friend scored more runs than you.

Worked Example

Step-by-Step

Let's check if the inequality "15 + 5 < 25" is true or false.

Step 1: First, solve the left side of the inequality. We have 15 + 5.

Step 2: 15 + 5 = 20.

Step 3: Now, rewrite the inequality with the solved left side: 20 < 25.

Step 4: Look at the comparison: Is 20 less than 25?

Step 5: Yes, 20 is indeed less than 25.

Answer: The inequality "15 + 5 < 25" is a true inequality.

Why It Matters

Understanding inequalities helps in making smart decisions every day, from managing your pocket money to planning a trip. Professionals in finance use inequalities to check if investments are profitable, and engineers use them to ensure structures are safe. Even game developers use inequalities to decide if a player has enough points to unlock a new level!

Common Mistakes

MISTAKE: Confusing '>' with '<' | CORRECTION: Remember, the open mouth of the symbol always points towards the larger number. Think of it like a hungry crocodile eating the bigger meal.

MISTAKE: Forgetting to simplify both sides before comparing | CORRECTION: Always calculate the total value of each side of the inequality first, just like solving a sum, then compare the final numbers.

MISTAKE: Thinking an inequality must always have a variable (like x or y) | CORRECTION: Inequalities can compare just numbers, like '10 > 5'. They don't always need letters.

Practice Questions

Try It Yourself

QUESTION: Is the inequality "7 + 3 > 12" true or false? | ANSWER: False

QUESTION: Which symbol makes the statement true: 20 ___ 15 + 6? (Choose from <, >, or =) | ANSWER: <

QUESTION: Your school library has 45 storybooks and 30 science books. If a friend says "The number of storybooks is less than 40", is this a true inequality? | ANSWER: No, it's false because 45 is not less than 40.

MCQ

Quick Quiz

Which of the following is a true inequality?

10 < 5

8 + 2 > 15

7 + 4 = 11

12 > 9

The Correct Answer Is:

Option D, '12 > 9', is true because 12 is indeed greater than 9. Options A and B are false inequalities, and Option C is an equality, not an inequality.

Real World Connection

In the Real World

When you buy groceries, the shopkeeper might tell you, 'You need to pay Rs 100 or more to use UPI.' This is an inequality! It means your bill amount (let's say 'B') must satisfy B >= 100 for you to use UPI. If your bill is Rs 80, then 80 >= 100 is false, so you can't use UPI.

Key Vocabulary

Key Terms

INEQUALITY: A statement comparing two values that are not equal | GREATER THAN (>): Means a number is larger than another | LESS THAN (<): Means a number is smaller than another | TRUE: Correct, valid, accurate | FALSE: Incorrect, not valid, inaccurate

What's Next

What to Learn Next

Now that you understand what a true inequality is, you're ready to learn about solving simple inequalities with variables. This will help you find a range of possible answers for real-world problems, making math even more useful!