Sure, let's break down each statement to determine which describe the characteristics of an AND inequality:
1. Values in the solution set satisfy both inequalities.
- In an AND inequality, the solution set is composed of values that must satisfy both of the given inequalities simultaneously. For example, if you have the inequalities [tex]\( x > 1 \)[/tex] and [tex]\( x < 5 \)[/tex], the solution set would be the intersection of these two inequalities: [tex]\( 1 < x < 5 \)[/tex]. The values within this interval satisfy both [tex]\( x > 1 \)[/tex] and [tex]\( x < 5 \)[/tex].
2. Shading generally occurs to the right or the left of the named values.
- This statement is more characteristic of an OR inequality. In an OR inequality, the solution covers a wider range and the shading can extend to the right or left of the named values, rather than being confined between them.
3. It is the union of two solution sets.
- This statement describes an OR inequality. In an OR inequality, any value that satisfies either one of the inequalities is included in the solution set, making it a union of the two sets.
4. It is the intersection of two solution sets.
- This is indeed characteristic of an AND inequality. For an AND inequality, the solution set consists of the values that are common to both inequalities, which means it is the intersection of the two solution sets.
Summarizing the correct statements that describe characteristics of an AND inequality:
- Values in the solution set satisfy both inequalities.
- It is the intersection of two solution sets.
Hence, the answer is:
1. Values in the solution set satisfy both inequalities.
4. It is the intersection of two solution sets.
