Inequalities - IELTS Academic Writing IELTS Study Notes
Overview
Imagine you're sharing pizza with friends, but some friends want more slices than others, or you need to make sure everyone gets at least two slices. That's where inequalities come in! They help us describe situations where things aren't exactly equal, but rather 'more than,' 'less than,' 'at least,' or 'at most.' In IELTS Academic Writing, especially when you're describing charts, graphs, or data, you'll often need to talk about things that are not exactly the same. For example, you might say 'the number of students increased to more than 500' or 'fewer than 10% of people agreed.' Inequalities give you the perfect tools to express these ideas clearly and accurately. Understanding inequalities helps you write more precise and sophisticated sentences, showing the examiner you can handle complex data descriptions. It's like having a special set of words to paint a clearer picture of numbers and trends.
What Is This? (The Simple Version)
Think of inequalities like a seesaw that isn't perfectly balanced. Instead of saying two things are exactly the same (like 5 = 5), inequalities tell us if one side is heavier or lighter than the other. They use special symbols to show these relationships.
Here are the main symbols you'll see:
- > means 'greater than' (the left side is bigger than the right side, like 7 > 3)
- < means 'less than' (the left side is smaller than the right side, like 2 < 8)
- ≥ means 'greater than or equal to' (the left side is bigger than or the same as the right side, like 5 ≥ 5 or 6 ≥ 4)
- ≤ means 'less than or equal to' (the left side is smaller than or the same as the right side, like 3 ≤ 3 or 1 ≤ 9)
So, instead of just saying 'the temperature was 20 degrees,' you might say 'the temperature was greater than 20 degrees' (T > 20) or 'the temperature was at most 25 degrees' (T ≤ 25). It's all about showing a range or a comparison, not just an exact match.
Real-World Example
Let's imagine you're planning a birthday party, and you need to buy drinks. The store has a special offer: you get a discount if you buy at least 10 bottles of juice. This 'at least 10' is an inequality!
Here's how it works:
- What's the rule? You need to buy 'at least 10 bottles.'
- What does 'at least' mean? It means 10 bottles is okay, but more than 10 bottles is also okay. You just can't buy 9 or fewer.
- Which symbol fits? Since 10 is allowed, and anything greater than 10 is allowed, we use the 'greater than or equal to' symbol (≥).
- Putting it together: If 'B' stands for the number of bottles you buy, then the rule is B ≥ 10. This means B can be 10, 11, 12, and so on. If you bought 9 bottles (B=9), you wouldn't get the discount because 9 is not ≥ 10.
How It Works (Step by Step)
When you see inequalities in a sentence, here's how to understand them: 1. **Identify the numbers:** Look for the quantities or limits mentioned (e.g., 'more than 50,' 'under 10%'). 2. **Find the comparison word:** Look for words like 'greater than,' 'less than,' 'at least,' 'at most,' 'exceeds,' ...
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Key Concepts
- Inequality: A mathematical statement showing that two expressions are not equal, using symbols like >, <, ≥, or ≤.
- Greater Than (>): A symbol meaning one value is larger than another (e.g., 5 > 3).
- Less Than (<): A symbol meaning one value is smaller than another (e.g., 2 < 6).
- Greater Than or Equal To (≥): A symbol meaning one value is larger than or the same as another (e.g., 7 ≥ 7 or 7 ≥ 5).
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Exam Tips
- →When describing trends in graphs, use inequality phrases like 'rose to more than 20%' or 'fell to less than half' to show precision.
- →Practice converting common phrases (e.g., 'exceeded,' 'below,' 'minimum') into their correct inequality symbols to improve accuracy.
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