What is an Inequality?

S3-SA1-0050

Grade Level:

Class 6

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

Definition

What is it?

An inequality is a mathematical statement that shows one value or expression is not equal to another. Instead of an equals sign (=), it uses symbols like greater than (>), less than (<), greater than or equal to (>=), or less than or equal to (<=) to compare values.

Simple Example

Quick Example

Imagine your favourite cricket team needs to score more than 150 runs to win a match. If 'R' is the runs scored, then R > 150 is an inequality. It means the runs must be any number greater than 150, like 151, 152, or even 200, but not exactly 150 or less.

Worked Example

Step-by-Step

PROBLEM: Your mobile data plan gives you a maximum of 2 GB (Gigabytes) per day. If 'D' represents the data you use, write an inequality to show how much data you can use.

STEP 1: Identify the quantity being measured. Here, it's 'D' for data used.
---STEP 2: Identify the limit or condition. The maximum data is 2 GB.
---STEP 3: Decide how the quantity relates to the limit. You can use 2 GB or less than 2 GB, but not more.
---STEP 4: Choose the correct inequality symbol. 'Less than or equal to' (<=) fits this situation.
---STEP 5: Write the inequality. D <= 2
---ANSWER: The inequality is D <= 2. This means you can use 2 GB, 1.5 GB, 0.5 GB, or any amount up to 2 GB.

Why It Matters

Inequalities help us make decisions and set limits in many fields. Engineers use them to design structures that can handle a certain amount of weight, and economists use them to understand market trends. Even computer scientists use inequalities to set conditions in programming, making apps and games work!

Common Mistakes

MISTAKE: Confusing '>' with '>=' | CORRECTION: '>' means 'strictly greater than' (e.g., 5 > 4, but not 5 > 5). '>=' means 'greater than or equal to' (e.g., 5 >= 4 and 5 >= 5). The line underneath means 'or equal to'.

MISTAKE: Reading the inequality symbol incorrectly | CORRECTION: The 'open mouth' of the symbol always points towards the larger number. For example, 7 > 3 means 7 is greater than 3. You can also think of it as an alligator eating the bigger number.

MISTAKE: Thinking an inequality only has one answer | CORRECTION: Unlike equations, inequalities usually have many possible solutions. For example, x < 5 means x can be 4, 3, 2.5, 0, -100, and so on.

Practice Questions

Try It Yourself

QUESTION: A bus can carry at most 50 passengers. If 'P' is the number of passengers, write an inequality. | ANSWER: P <= 50

QUESTION: To qualify for the school sports team, a student must be at least 11 years old. If 'A' is the student's age, write an inequality. | ANSWER: A >= 11

QUESTION: A shop offers a discount if you spend more than ₹500. If 'S' is the amount spent, write an inequality for getting the discount. Then, list two possible amounts you could spend to get the discount. | ANSWER: S > 500. Possible amounts: ₹501, ₹600 (any number greater than 500)

MCQ

Quick Quiz

Which symbol means 'less than or equal to'?

The Correct Answer Is:

The symbol '<=' has a line underneath the '<' sign, which indicates 'or equal to'. Options A and C mean 'greater than' and 'greater than or equal to' respectively, while B means 'less than'.

Real World Connection

In the Real World

When you use a food delivery app like Zomato or Swiggy, the app might show restaurants within a certain distance, say 'less than 5 km'. This uses an inequality to filter options. Also, traffic signals use inequalities – if the timer shows 'time remaining <= 5 seconds', it's about to change!

Key Vocabulary

Key Terms

GREATER THAN (>): A symbol showing one value is larger than another | LESS THAN (<): A symbol showing one value is smaller than another | GREATER THAN OR EQUAL TO (>=): A symbol showing one value is larger than or the same as another | LESS THAN OR EQUAL TO (<=): A symbol showing one value is smaller than or the same as another | SOLUTION SET: The range of values that satisfy an inequality

What's Next

What to Learn Next

Great job understanding inequalities! Next, you can learn how to solve simple inequalities, which is similar to solving equations but with a few important differences. This will help you find the exact range of values that make an inequality true.