Here are the essential concepts you must grasp in order to answer the question correctly.
Compound Inequalities
A compound inequality consists of two or more inequalities that are combined into one statement by the words 'and' or 'or'. In this case, the compound inequality involves both a strict inequality (<) and a non-strict inequality (≤), which must be solved simultaneously to find the values of the variable that satisfy both conditions.
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Solving Inequalities
Solving inequalities involves isolating the variable on one side of the inequality sign. This process is similar to solving equations, but one must remember that multiplying or dividing by a negative number reverses the inequality sign. Understanding how to manipulate inequalities is crucial for finding the solution set.
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Interval Notation
Interval notation is a way of representing the solution set of an inequality using intervals. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). This notation is essential for clearly expressing the range of values that satisfy the compound inequality.
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