#### Chapter 3 Inequalities in one Variable

**Section 3.1 Inequalities and their Solution Sets**

# 3.1.1 Introduction

##### **Info 3.1.1 **

If two numbers are related by one of the

**comparators**$\le $, $<$, $\ge $, or $>$, a statement is generated that can be true or false depending on the numbers:

- $a<b$ (reads: "$a$ is strictly less than $b$" or simply "$a$ is less than $b$") is true if the number $a$ is less than and not equal to $b$.

- $a\le b$ (reads: "$a$ is less than $b$") is true if $a$ is less than or equal to $b$.

- $a>b$ (reads: "$a$ is strictly greater than $b$" or simply "$a$ is greater than $b$") is true if the number $a$ is greater and not equal to $b$.

- $a\ge b$ (reads: "$a$ is greater than $b$") is true if the number $a$ is greater than or equal to $b$.

The comparators describe how the given values are related to each other on the number line: $a<b$ means that $a$ is to the left of $b$ on the number line.

Here, $a<b$ means the same as $b>a$, likewise $a\le b$ means the same as $b\ge a$. But it should be noted that the opposite of the statement $a<b$ is the statement $a\ge b$ and not $a>b$. If terms with a variable occur in an inequality, the problem is to find the number range of the variable such that the inequality is true.