Objectives
To solve and graph inequalities
To write and solve compound inequalities
Solving Inequalities
Compound Inequalities
Words like “at most” and “at least” suggest a relationship in which two quantities may not be equal. You can represent such a relationship with a mathematical inequality.
Essential Understanding Just as you use properties of equality to solve equations, you can use properties of inequality to solve inequalities.
Inequality | Word Sentence | Graph |
---|---|---|
|
x is greater than 4. |
Image Long Description |
|
x is greater than or equal to 4. | |
|
x is less than 4. | |
|
x is less than or equal to 4. |
In the graphs above, the point at 4 is a boundary point because it separates the graph of the inequality from the rest of the number line. An open dot at 4 means that 4 is not a solution. A closed dot at 4 means that 4 is a solution.