Chapter 3 Inequalities in one Variable Section 3.1 Inequalities and their Solution Sets
If two numbers are related by one of the comparators , , , or , a statement is generated that can be true or false depending on the numbers:
- (reads: " is strictly less than " or simply " is less than ") is true if the number is less than and not equal to .
- (reads: " is less than ") is true if is less than or equal to .
- (reads: " is strictly greater than " or simply " is greater than ") is true if the number is greater and not equal to .
- (reads: " is greater than ") is true if the number is greater than or equal to .
The comparators describe how the given values are related to each other on the number line: means that is to the left of on the number line.
Here, means the same as , likewise means the same as . But it should be noted that the opposite of the statement is the statement and not . 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.