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 use 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 involving ranges of values.
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Graphing Inequalities
Graphing inequalities involves representing the solution set of an inequality on a number line or coordinate plane. For example, the inequality −2 ≤ x < 5 would be graphed by shading the region between -2 and 5 on a number line, including -2 but not 5. This visual representation helps in understanding the range of possible solutions.
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Solution Sets
A solution set is the collection of all values that satisfy a given inequality or system of inequalities. In the case of the inequality −2 ≤ x < 5, the solution set includes all real numbers from -2 to 5, where -2 is included and 5 is excluded. Identifying and expressing solution sets is crucial for solving and graphing inequalities accurately.
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Categorizing Linear Equations