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 equal. They can be represented using symbols such as '>', '<', '≥', and '≤'. Solving inequalities involves finding the values of the variable that make the inequality true, which often requires manipulating the expressions similarly to equations.
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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 (2, 5] includes all numbers greater than 2 and up to 5, including 5 but not 2.
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Rational Expressions
Rational expressions are fractions where the numerator and denominator are polynomials. In the given inequality, the expression (3x - 2)/(x - 4) is a rational expression. Understanding how to analyze and manipulate rational expressions is crucial for solving inequalities involving them, particularly in determining where the expression is positive or negative.
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Rationalizing Denominators