Please get ready and settle in. Understanding and solving inequalities. You might be wondering, 'What is an inequality?' It's simply a way of comparing things. We do this all the time, don't we? We say one box is heavier, one friend is taller. In math, we use special symbols to write these comparisons. This is our learning goal. By the end of the lesson, you should be comfortable using symbols like the less than sign, the greater than sign, and their 'or equal to' versions to compare numbers. It's like learning a new, precise language for talking about size and quantity. The most important question you might ask is, 'Why should we care about this?' I'm glad you asked! This box tells us exactly why it matters. We see inequalities in everyday Kenya. Think about the voting age: you must be 18 years or older. That's an inequality! The age (A) must be greater than or equal to 18. What about lorry loads? A matatu has a sign saying 'Maximum 14 passengers'. That means the number of people must be less than or equal to 14. Even when shopping, you compare prices to see which is cheaper. This isn't just a textbook idea; it's all around us! Here's a quick preview of the key symbols we'll be using, to give you a head start.
Let's build on the idea of comparing numbers. This next slide gives us the language we need. The first symbol is 'less than', this little pointed arrow pointing left. It means the number on the left is smaller than the number on the right. 5 is less than 10, we write it like this. The small, sharp end points to the smaller number. Next we have 'less than or equal to'. See the extra line underneath? That means it can be less than, OR it can be equal. The same logic applies for 'greater than or equal to'. 4 is less than or equal to 4. Is that true? The symbol allows for that. Time to put it into practice. Five is less than ten. Eight is greater than three. Four is less than or equal to four. Seven is greater than or equal to five. Good practice. Always ask yourself those key questions: which number is smaller? Which is larger? That will tell you which symbol to use.
Before we begin today, I'd like to check something. Show of hands, who has ever read a word problem and immediately felt a bit confused? That's okay; many of us feel that way. Words are for stories, but math uses symbols. Today, we will build a bridge between them. Our goal: to learn how to translate real-world Kenyan situations, described in words, into clear mathematical inequalities. Our first, and most crucial, step is to identify the unknown. For the question the problem is asking. What do we need to find? It could be a person's age, the amount of money, or the number of items. We choose a letter—usually 'x'—to represent that mystery quantity. Think of 'x' as the character in our story whose name we don't know yet. Just like this example. 'A person's age?' That's our unknown. We declare: 'Let x equal age.' It's simple. We've just given the mystery a name. Step two: Find the key words. This is where you become a word detective. We're not looking for 'answer' or 'find', but for phrases that tell us about relationships. Words like 'minimum', 'at least', 'more than', 'less than', 'maximum', or 'not exceeding'. These are the words that will tell us which inequality symbol to use—greater than, less than, and so on. Finally, step three. We build the inequality. We combine our named unknown, 'x', with the relationship we found using the key words. We write it using symbols like >, <, ≥, or ≤. This mathematical sentence is the translation of our story. Let's apply our three steps to a very important, real Kenyan example. Voting in elections. Here is our word problem: 'You must be at least 18 years old to vote.' Okay, team, let's walk through it. Step one, what is the unknown? Good, the voter's age. Let x equal the voter's age. Step two, find the key words. 'At least.' This is a major clue. 'At least' means the minimum is 18; you can be 18 or more. Step three, building. We put it together: 'x is at least 18' becomes... X is greater than or equal to 18. Or, x ≥ 18. That simple line, x ≥ 18, is the complete mathematical language for that entire rule about voting. From a sentence full of words, we have built a clean, powerful mathematical statement.
Solving inequalities, which is a crucial skill in algebra. Our topic for this page is our 'Golden Rule' for dealing with them.
This is our summary and next steps. We've mastered Key Skill One: using the inequality symbols. Less than, greater than, less than or equal to, and greater than or equal to. Remember, these symbols are just like a judge in a race. 'Seven' is definitely greater than 'four'. 'x less than or equal to ten' means x can be any number from ten all the way down. For Key Skill Two, the most important thing is: your actions must be fair to both sides, just like sharing oranges fairly. The golden rule: you must flip that inequality sign when you multiply or divide by a negative number. Like in this example: negative three x is greater than six. To solve it, we divide both sides by negative three. Because we divided by a negative, the 'greater than' sign flips and becomes a 'less than'. It's like a magic trick, but with a very logical reason. Finally, I want you to remember this: mathematics helps us understand the world. It's the language of the rules around us. The voting age rule, 'you must be at least 18'. The rule for safe driving weight, 'your lorry cannot weigh more than 20 tonnes'. These are all real-life inequalities that keep our society organised and safe. Great work everyone. This connects us perfectly back to our KICD strand.
