Problem 134 - College Algebra Essentials

Question

When graphing the solutions of an inequality, what does a parenthesis signify? What does a square bracket signify?

Step-by-Step Solution

Answer

The parenthesis, when graphing the solutions of an inequality, signifies an open interval that does not include the endpoint value. The square bracket, under the same circumstances, signifies a closed interval, indicating inclusion of the endpoint value.

Step 1: Understand Parentheses ( )

A parenthesis, or round bracket, is used when graphing the solutions of an inequality to denote an open interval. This means the end point value would not be included in the solution set. For instance, when stating that a solution lies in the interval \( (2, 5) \), it means the solution consists all the values between 2 and 5, excluding the numbers 2 and 5 themselves.

Step 2: Understand Brackets [ ]

A bracket, or square bracket, is used when graphing the solutions of an inequality to denote a closed interval. This indicates that the end point value is included in the solution set. For instance, if the solution is said to be in the interval \([3, 7]\), it means the solution includes all the values between 3 and 7, including 3 and 7 themselves.

Step 3: Combine understanding of Parentheses and Brackets

In some cases, a combination of a parenthesis and bracket may be used for an interval. For example, \([3, 7)\) indicates the solution includes all values between 3 and 7, including 3 but excluding 7. Conversely, \((3, 7]\) indicates that solution includes all values between 3 and 7, excluding 3 but including 7.