Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical statements that express the relationship between two expressions that are not necessarily equal. They use symbols such as ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than). Solving inequalities involves finding the values of the variable that make the inequality true, which can include a range of values rather than a single solution.
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Algebraic Manipulation
Algebraic manipulation refers to the process of rearranging and simplifying algebraic expressions to isolate the variable of interest. This includes operations such as distributing, combining like terms, and moving terms from one side of the inequality to the other. Mastery of these techniques is essential for solving inequalities effectively and accurately.
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Introduction to Algebraic Expressions
Interval Notation
Interval notation is a mathematical notation used to represent a range of values on the number line. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, the interval (a, b] includes all numbers greater than a and up to b, including b itself. Understanding interval notation is crucial for expressing the solution set of inequalities clearly.
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