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What is a Range of Values (Satisfying an Inequality)?
Grade Level:
Class 5
Maths, Computing, AI, Logic, Data Science
Definition
What is it?
A 'range of values' means all the possible numbers that fit a certain rule or condition. When we talk about a range satisfying an inequality, it means all the numbers that make a mathematical statement (like 'greater than' or 'less than') true.
Simple Example
Quick Example
Imagine your mom says you can buy a toy that costs 'more than Rs. 100 but less than Rs. 200'. The range of values for the toy's price would be all amounts like Rs. 101, Rs. 102, all the way up to Rs. 199. Any price in this range makes your mom's rule true.
Worked Example
Step-by-Step
Let's find the range of whole numbers (integers) 'x' that satisfy the inequality: x > 5 and x < 10.
Step 1: Understand the first part: x > 5. This means 'x' must be greater than 5. So, numbers like 6, 7, 8, 9, 10, and so on, are possible.
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Step 2: Understand the second part: x < 10. This means 'x' must be less than 10. So, numbers like 9, 8, 7, 6, 5, and so on, are possible.
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Step 3: Now, we need numbers that satisfy BOTH conditions at the same time. They must be greater than 5 AND less than 10.
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Step 4: Let's list numbers greater than 5: 6, 7, 8, 9, 10, 11...
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Step 5: Let's list numbers less than 10: ...6, 7, 8, 9.
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Step 6: The numbers that appear in both lists are 6, 7, 8, 9.
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Answer: The range of whole numbers 'x' is {6, 7, 8, 9}.
Why It Matters
Understanding ranges helps you make smart decisions in daily life and is super important in fields like computer programming, data science, and AI. For example, coders use ranges to set conditions for how apps work, and data scientists use them to filter information, which can even help predict cricket match outcomes!
Common Mistakes
MISTAKE: Including the boundary numbers when the inequality is 'strictly greater than' or 'strictly less than' (e.g., x > 5, including 5) | CORRECTION: If it's '>', '<', then the boundary number itself is NOT included. If it's '>=' or '<=', then the boundary number IS included.
MISTAKE: Only considering one part of a combined inequality (e.g., for 5 < x < 10, only looking at x < 10) | CORRECTION: For combined inequalities, remember that the variable must satisfy ALL parts of the inequality at the same time.
MISTAKE: Confusing 'greater than' (>) with 'greater than or equal to' (>=) | CORRECTION: '>' means the number must be strictly bigger. '>=' means it can be bigger OR exactly equal to the number.
Practice Questions
Try It Yourself
QUESTION: What is the range of whole numbers 'y' such that y >= 3 and y < 7? | ANSWER: {3, 4, 5, 6}
QUESTION: A mobile phone plan offers free data if your usage 'd' is less than 5 GB. If 'd' is measured in whole GBs, what is the range of data usage for free data? | ANSWER: {0, 1, 2, 3, 4}
QUESTION: Your school library allows you to borrow books if your age 'a' is at least 10 years and at most 14 years. Write this as an inequality and list the range of whole number ages. | ANSWER: 10 <= a <= 14; Range: {10, 11, 12, 13, 14}
MCQ
Quick Quiz
Which of the following numbers is NOT in the range of whole numbers 'p' where 8 < p <= 12?
9
10
12
8
The Correct Answer Is:
D
The inequality 8 < p <= 12 means 'p' must be greater than 8 (so 8 is not included) and less than or equal to 12 (so 12 is included). Thus, 8 is not in the range.
Real World Connection
In the Real World
When you use a filter on an online shopping app like Flipkart or Amazon to find t-shirts between Rs. 300 and Rs. 500, you are using a range of values. The app's computer program uses inequalities to show you only the items that fit your price range.
Key Vocabulary
Key Terms
RANGE: All possible values that fit a rule | INEQUALITY: A mathematical statement showing one value is not equal to another (e.g., greater than, less than) | WHOLE NUMBERS: Numbers without fractions or decimals (0, 1, 2, 3...) | SATISFY: To make a condition or rule true
What's Next
What to Learn Next
Great job understanding ranges! Next, you can explore 'Solving Simple Inequalities'. This will teach you how to find these ranges when the variable is part of a more complex math problem, which is a key skill for higher classes.
