Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They can be represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Understanding how to interpret and manipulate inequalities is essential for solving problems that involve ranges of values.
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Interval Notation
Interval notation is a way of representing a set of numbers between two endpoints. It uses parentheses and brackets to indicate whether the endpoints are included (closed interval) or excluded (open interval). For example, the interval (-∞, -6) represents all numbers less than -6, which corresponds to the inequality x < -6.
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Graphing Inequalities
Graphing inequalities involves representing the solutions of an inequality on a number line. For the inequality x < -6, the graph would show an open circle at -6 (indicating that -6 is not included) and a shaded line extending to the left, representing all values less than -6. This visual representation helps in understanding the range of solutions that satisfy the inequality.
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