3. Numbers \( a \) and \( b \) are located to the left of \( c \) on a number line. Select all the inequalities that could be true. (A) \( a

Ask by Rogers Logan. in the United States

Jan 22,2025

To determine which inequalities could be true given that numbers \( a \) and \( b \) are located to the left of \( c \) on a number line, we need to understand the implications of their positions. Since \( a \) and \( b \) are both to the left of \( c \), we can conclude that: - \( a < c \) - \( b < c \) Now, let's analyze each option: (A) \( a < b < c \): This is possible if \( a \) is less than \( b \), and both are less than \( c \). This inequality could be true. (B) \( b < c < a \): This is not possible because \( c \) cannot be to the left of \( a \) if both \( a \) and \( b \) are to the left of \( c \). This inequality cannot be true. (C) \( c < a < b \): This is also not possible for the same reason as option B. This inequality cannot be true. (D) \( a = b \) and \( b < c \): This is possible. If \( a \) and \( b \) are equal and both are less than \( c \), this inequality could be true. (E) \( b < a < c \): This is possible if \( b \) is less than \( a \), and both are less than \( c \). This inequality could be true. Based on this analysis, the inequalities that could be true are: - (A) \( a < b < c \) - (D) \( a = b \) and \( b < c \) - (E) \( b < a < c \) Thus, the correct answers are (A), (D), and (E).