Problem 113 - Introductory Algebra for College Students

Question

When graphing the solutions of an inequality, what is the difference between a parenthesis and a bracket?

Step-by-Step Solution

Answer

In the context of graphing solutions of an inequality, a parenthesis is used to exclude the endpoint from the solution, while a bracket is used to include the endpoint in the solution.

Step 1: Parenthesis Use in Inequalities

A parenthesis '(' or ')' is used when graphing an inequality to indicate that the endpoint is not part of the solution. For example, if one was to graph the inequality \(x > 5\), then a parenthesesis '(' would be placed above the number 5 on the number line. This indicates that the solution includes all numbers greater than 5 but not 5 itself.

Step 2: Bracket Use in Inequalities

A bracket '[' or ']' is used when graphing an inequality to indicate that the endpoint is included in the solution. For instance, if one was to graph the inequality \(x \geq 5\), then a bracket '[' would be placed above the number 5 on the number line. This shows that the solution includes 5 and all numbers greater than 5.

Step 3: Summary of Parenthesis and Bracket Use

The difference between a parenthesis and a bracket in graphing solutions of an inequality lies in whether or not the endpoint is included in the solution; parenthesis '(' or ')' exclude the endpoint, while brackets '[' or ']' include it.