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Chapter 0: Problem 124

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

Short Answer

Expert verified
In graphing solutions of an inequality, a parenthesis signifies that the endpoint is not included in the solution set while a square bracket indicates that the endpoint is included in the solution set.

Step by step solution

01

Define Parentheses

Parentheses ( ) are used in an interval notation to represent that an endpoint of the interval is not included in the set. If you see a parenthesis on a number line graph or in interval notation, it means that the number right next to it is not part of the solution set.
02

Define Square Bracket

Square brackets [ ] on the other hand, are used to indicate that an endpoint of the interval is included in the set. If there is a square bracket shown on a number line graph or in interval notation, it signifies that the number next to the bracket is part of the solution set.
03

Application

For example, in the inequality solution \( x > 2 \), the number 2 would be represented in a graph or interval notation with a parenthesis ( ). It falls into the interval (2, +inf), meaning 2 is not included in the solution. But for the inequality solution \( x \ge 4 \), the number 4 would be represented with a square bracket, as in [4, +inf), meaning 4 is included in the solution.

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