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Interval notation is a way to represent a range of numbers using parentheses \( () \) and brackets \( [] \).
An open parenthesis \( ( \) means that the endpoint is not included in the interval. A closed bracket \( ] \) means that the endpoint is included.
For example, in the interval \( (-\frac{5}{6}, 4] \), -5/6 is not included (open parenthesis), and 4 is included (closed bracket).
The interval notation \( (-\frac{5}{6}, 4] \) reads as 'all numbers between -5/6 and 4, where -5/6 is not included but 4 is included'.

An inequality is a mathematical statement that compares two values that may not be equal. In interval notation, we transform the range of values into an inequality.
For the interval \( (-\frac{5}{6}, 4] \), we convert it into the inequality form as follows:
\(-\frac{5}{6} < x \leq 4 \)
Here, the variable \( x \) represents any number within the specified range. This inequality reads as 'x is greater than -5/6 and less than or equal to 4'.

Algebra involves the use of symbols and letters to represent numbers and quantities in formulas and equations. It's a fundamental part of math that helps in understanding and solving equations.
In our exercise, we used algebra to express the interval in set-builder notation.
Set-builder notation is a precise way to define a set by stating the properties that its members must satisfy.
The set-builder notation for the interval \( (-\frac{5}{6}, 4] \) is \{ x | -\frac{5}{6} < x \leq 4 \}
This reads as 'the set of all x such that -5/6 is less than x and x is less than or equal to 4'.
This notation combines algebra (inequality) with set theory to provide a clear, concise representation of the numbers within the given range.