Express the solution in interval notation.
A. [ $6,-5$ ]
B. [-5, 6]
C. $(-5,6)$
D. $(6,-5)$
Answer (2)
The correct interval notation from the options provided is [-5, 6], which represents the closed interval including both endpoints. Option C, (-5, 6), is also valid but excludes the endpoints. Ultimately, [-5, 6] is the most inclusive representation of the solution range.
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Interval notation represents a set of real numbers.
The left endpoint must be less than or equal to the right endpoint.
Square brackets [ ] include the endpoint, while parentheses ( ) exclude it.
The correct interval notation from the given options is [ − 5 , 6 ] .
Explanation
Understanding the Problem The problem asks us to express a solution in interval notation, given four options. We need to identify the correct interval notation from the provided choices.
Key Concepts of Interval Notation Interval notation represents a set of real numbers using endpoints and brackets or parentheses. The left endpoint must be less than or equal to the right endpoint. Square brackets [ ] indicate that the endpoint is included in the interval, while parentheses ( ) indicate that the endpoint is not included.
Analyzing the Options Let's examine the given options:
[ 6 , − 5 ]: This is invalid because the left endpoint (6) is greater than the right endpoint (-5).
[-5, 6]: This represents the closed interval from -5 to 6, including both -5 and 6. This is a valid interval notation.
( − 5 , 6 ): This represents the open interval from -5 to 6, excluding both -5 and 6. This is also a valid interval notation.
( 6 , − 5 ): This is invalid because the left endpoint (6) is greater than the right endpoint (-5).
Determining the Correct Interval Without additional context or information about the specific solution being represented, we cannot definitively choose between [-5, 6] and ( − 5 , 6 ) . However, since the problem does not provide any context, we can assume that the correct answer is simply asking for a valid interval notation.
Examples
Interval notation is used in various fields, such as calculus, to describe the domain and range of functions. For example, if a function is defined for all real numbers between -2 and 5, including -2 but excluding 5, we can represent its domain in interval notation as [-2, 5). This notation helps to clearly communicate the set of values for which the function is valid.
