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Chapter 6: Problem 95

When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot?

Short Answer

Expert verified
When graphing inequalities, an open dot signifies a number that is not part of the solution set, typically used with 'greater than' or 'less than' inequalities. In contrast, a closed dot, used with 'greater than or equal to' or 'less than or equal to' inequalities, represents a number that is included in the solution set.

Step by step solution

01

Understand the Concept of Open and Closed Dots

When we graph inequalities on a number line, we often use dots to represent the numbers that are included or excluded from the solution set. An open dot on a number represents a number that is not included in the solution set, while a closed dot means the number is included.
02

Understand the Usage

In more specific terms, when an inequality is 'greater than' or 'less than' (for example \(x > 2\) or \(x < 5\)), we use an open dot to signal that the number is not included in the solution set. Whereas, if the inequality is 'greater than or equal to' or 'less than or equal to' (like \(x \geq 6\) or \(x \leq 4\)), we use a closed dot to indicate inclusivity.
03

Practical Examples

As an instance, suppose we are graphing the inequality \(x > 3\). In this case, we put an open dot on the 3 to show that 3 is not part of the solution set. Conversely, if we were graphing \(x \geq 3\), we would place a closed dot on the 3 to demonstrate that 3 is included in the solution set.

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