Final answer:
Inequalities in math compare values and their solutions can be graphed. A filled-in dot or solid line indicates an inclusive boundary, while an open dot or dashed line indicates an exclusive boundary. Examples include graphing linear inequalities and using number lines to represent solution sets.
Step-by-step explanation:
The concept in question relates to inequalities in mathematics, specifically when graphing these inequalities on a coordinate system. An inequality is used to compare two values, often containing symbols such as ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than). When graphing an inequality, the largest or smallest value that is included in the solution set is typically represented with a filled-in dot or line, indicating that the value is part of the solution (equal to), whereas an open dot or dashed line shows that the value is not included (not equal to).
For example, consider the inequality 0 ≤ x ≤ 20. In this case, the graph of the function f(x) would be a horizontal line running between the vertical lines x = 0 and x = 20, where both endpoints would be represented with filled-in dots to indicate that the values 0 and 20 are included in the solution set.
Another example could be the statement "of the cars are at most that age" indicating an inequality such as x ≤ age, where you would sketch a number line and shade the region from negative infinity to the specified 'age', using a filled-in dot or a bracket at 'age' to denote that the cars' ages can be 'at most' that number.