Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Inequalities
Linear inequalities are mathematical expressions that involve a linear function and an inequality sign (such as ≤, ≥, <, or >). They represent a range of values rather than a single solution. Solving a linear inequality involves isolating the variable on one side of the inequality, similar to solving an equation, but requires special attention to the direction of the inequality when multiplying or dividing by negative numbers.
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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 (2, 5] includes all numbers greater than 2 and up to and including 5. Understanding how to express solution sets in interval notation is essential for clearly communicating the results of inequalities.
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Graphing on a Number Line
Graphing solution sets on a number line visually represents the range of values that satisfy an inequality. This involves marking points on the line to indicate included or excluded endpoints, using solid dots for included values and open dots for excluded values. Properly graphing the solution helps in understanding the relationship between the algebraic solution and its visual representation, making it easier to interpret the results.
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Graphing Lines in Slope-Intercept Form