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

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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).
The inequalities that could be true are: - (A) $$ a < b < c $$ - (D) $$ a = b $$ and $$ b < c $$ - (E) $$ b < a < c $$

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

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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