Final Answer:
The interval notation all numbers between -9 and 6, including -9 and excluding 6 is (−9,6].Thus the option C. \((-9, 6]\) is correct.
Step-by-step explanation:
The correct interval notation for all numbers between -9 and 6, including -9 and excluding 6, is represented by option C (−9,6]. The open parenthesis (−9 indicates that -9 is not included in the interval, while the closed bracket6] indicates that 6 is included in the interval. Therefore, the interval spans from -9 up to, but not including, 6.
To break down the notation, (−9,6], the open parenthesis (−9 signifies that -9 is part of the solution set, and the closing bracket 6] signifies that 6 is included in the interval. This notation is a concise and standardized way to represent a range of real numbers, making it clear which values are included and excluded.
In mathematical terms, the interval (−9,6] can be expressed as −9<x≤6, where x represents the variable within the specified range. This notation is essential in mathematics for clearly conveying intervals and sets of numbers, providing a standardized and unambiguous representation of the solution space.
Thus the option C. \((-9, 6]\) is correct.