The problem asks us to identify which number line model correctly represents the expression $5\frac{1}{2} + (-3)$.

1. Problem Description

The problem asks us to identify which number line model correctly represents the expression $5\frac{1}{2} + (-3)$.

2. Solution Steps

First, we need to evaluate the expression:

$5\frac{1}{2} + (-3) = 5.5 - 3 = 2.5$

Now, we need to examine the number lines to see which one correctly models the expression.

A) The first arrow starts at 0 and goes to -

6. The second arrow starts at -6 and goes left 3 units to -

9. This represents the expression $-6 + (-3) = -9$.

B) The first arrow starts at 0 and goes to 5.

5. The second arrow starts at 5.5 and goes left 3 units. The arrow ends at 2.

5. This number line model represents the expression $5.5 + (-3) = 2.5$.

C) The first arrow starts at 0 and goes to -

3. The second arrow starts at -3 and goes right 5.5 units. The arrow ends at 2.

5. This number line model represents the expression $-3 + 5.5 = 2.5$. However, we are looking for $5.5 + (-3) = 2.5$.

Since we are looking for $5\frac{1}{2} + (-3)$, the first arrow should start at 0 and go to $5\frac{1}{2}$. The second arrow should start from $5\frac{1}{2}$ and go to the left by 3 units. Therefore, option B is the correct number line.

3. Final Answer

B