Final answer:
The question addresses the mathematical concept of graphing a compound inequality on a number line using symbols such as union, intersection, subset, and superset. It involves identifying the value ranges that satisfy either at least one inequality (union) or all inequalities (intersection).
Step-by-step explanation:
The question involves graphing a compound inequality on a number line, which is a concept in mathematics. Before we discuss how to graph compound inequalities, it's important to understand some basic terms related to inequalities:
- Union (symbolized by ∪) - This represents all the elements that are in either set or both. In terms of inequalities, it means the values that satisfy at least one of the inequalities.
- Intersection (symbolized by ∩) - This indicates the elements that are common to both sets. For inequalities, it refers to the values that satisfy both inequalities at the same time.
- Subset (symbolized by ⊂) - A set A is a subset of set B if all elements of A are also elements of B.
- Superset (symbolized by ⊃) - A set A is a superset of set B if B is a subset of A, which means all elements of B are also elements of A.
When graphing compound inequalities, we look for the range of values that fulfill the condition set by the union or intersection of the inequalities. For a union, we combine the ranges on the number line where the inequalities are true. For an intersection, we only shade the overlapping region where both inequalities are true.
To graph an inequality, you typically use a circle to indicate whether a value is included (a filled circle) or not included (an unfilled circle) and a line to show the continuation of all values that satisfy the inequality. If the inequality is '<' or '>', you use an open circle; for '≤' or '≥', a closed circle is used.
In conclusion, the correct representation of a compound inequality on a number line involves utilizing either the union or intersection of the individual inequalities, as appropriate, and graphically signifying the range of values. The union or intersection is marked on the number line accordingly to clearly show the set of solutions for the compound inequality.