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When dealing with inequalities, interval notation is a concise way to represent a range of values that a variable can take. Instead of stating the inequality in words or symbols multiple times, interval notation uses a specific format to display the start and end points of an interval.

- **Parentheses** - Used when the endpoints are not included in the interval (often indicated by '<' or '>'). For example, in \((-5, 2)\). - **Brackets** - Used when the endpoints are included (often indicated by '\(\leq\)' or '\(\geq\)'). For instance, \([-5, 2]\) would mean \(-5\) and \(2\) are included.Dividing expressions into this format makes it very easy to read and understand which values are possible for a variable. It also helps in easy conversion of inequalities into a graphical format.

Compound inequalities are expressions that involve more than one inequality symbol. They show a range of values that satisfy multiple conditions simultaneously. In the given problem, the compound inequality \(-5 < x < 2\) tells us that - The value of \(x\) is greater than \(-5\)- The value of \(x\) is less than \(2\)By stating both conditions together, you indicate a specific range for \(x\), called a closed range. Within this range,\(x\) can be any number that meets both conditions without meeting the equalities on either side. In compound inequalities like this one, think of strings pulling \(x\) from both sides towards the center.

Graphing inequalities visually represents the solution set on a number line. This can help you better understand the range of possible values a variable can take. To graph an inequality like \(-5 < x < 2\), perform the following steps:- **Mark the Boundaries:** Put open circles at \(-5\) and \(2\) on the number line as these values are not included in the solution (indicated by the lack of equals in the inequality).- **Shade the Interval:** Draw a shaded line between the open circles to show all possible values for \(x\) that are within the inequality's bounds. This visual tool is particularly helpful because it gives a clear picture of which portions of the number line are solutions to the given inequality. This makes double-checking your work easier and more intuitive.