Lesson Notes By Weeks and Term v4 - JHS 2

Lesson Video

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Performance objectives

• Define a linear inequality.
• Solve simple linear inequalities.
• Represent solutions on a number line.
• Apply inequalities to real-life problems.

Lesson summary

In our daily lives, we are constantly comparing things. We compare prices at the market, the time it takes to get to school, or the scores in a football match. We often use words like "more than," "less than," "at least," or "at most." For example, to ride the "tro-tro," you must have *at least* the required fare. In mathematics, we use special symbols to represent these relationships. Today, we will learn how to solve problems involving these comparisons, which are called inequalities. This skill is very useful for making smart decisions about money, time, and many other things.

Lesson notes

A. What is an Inequality?

An inequality is a mathematical statement that compares two values that are not equal. While an equation uses an equal sign (=) to show that two expressions have the same value (e.g., `x + 2 = 5`), an inequality uses a symbol to show the relationship between them. B. The Four Inequality Symbols

There are four main symbols we use in inequalities:

| Symbol | Meaning | Example | Reading the Example | | :----: | ----------------------- | -------------- | ------------------------------ | | > | Greater than | `x > 5` | "x is greater than 5" | | ** and 10`. Goal: Get `x` by itself. Action: To get rid of `-4`, we must add `4` to both sides. Calculation: ``` x - 4 > 10 x - 4 + 4 > 10 + 4 x > 14 ``` Solution Set: The solution is all numbers greater than 14. This means 14.1, 15, 20, 100, and so on, are all possible solutions. We write the solution set as `x > 14`.