Question

which problem is modeled on the number line? -5 -4 -3 -2 -1 0 1 2 3 4 5 -3 + (-6) -3 + 6 3 + (-6) 3 + 6

Explanation:

Step1: Analyze the number line movements

The red arrow starts at 0 and moves left 3 units to -3 (or starts at -3? Wait, the blue arrow: let's see the directions. Wait, the red arrow is moving left (negative direction) and blue? Wait, no, the number line: the red segment is from -3 to 0? Wait, no, the arrows: the red arrow is pointing left, length from -3 to 0? Wait, no, the blue arrow is pointing right, length from -3 to 3? Wait, no, let's check the operations. Let's recall that on a number line, adding a positive number moves right, adding a negative moves left.

First, let's see the starting point. The red arrow: if we consider the first movement, maybe starting at -3? Wait, no, the blue arrow is longer. Wait, the options: let's compute each option.

Option 1: $-3 + (-6) = -9$ (too far left, not matching the number line which goes to -5 to 5)
Option 2: $-3 + 6$: start at -3, move right 6 units: $-3 + 6 = 3$. Let's check the number line: from -3, moving right 6 (since +6 is right) would end at 3. The blue arrow goes from -3 to 3 (6 units right), and the red? Wait, maybe the first movement is to -3, then adding 6. Wait, the red arrow: maybe the initial position? Wait, the number line has a red arrow from -3 to 0? No, the red arrow is pointing left, length from -3 to 0? Wait, no, the blue arrow is from -3 to 3 (6 units right). So starting at -3, adding 6 (since +6 is right) gives 3, which matches the blue arrow going from -3 to 3. Let's check other options.

Option 3: $3 + (-6) = -3$. Start at 3, move left 6: ends at -3. But the number line's red arrow is not starting at 3.

Option 4: $3 + 6 = 9$ (too far right).

So $-3 + 6$: start at -3, move right 6 (since +6 is positive, right direction) to 3. Which matches the blue arrow going from -3 to 3 (6 units right), and maybe the red arrow was the starting point or a previous move? Wait, the number line's red arrow: maybe the initial position is -3? Wait, the red arrow is pointing left, but maybe the first step is to -3, then adding 6. So $-3 + 6$ is the operation.

Step2: Verify each option

• $-3 + (-6) = -9$: not on the number line (max -5).
• $-3 + 6 = 3$: start at -3, move right 6 (from -3 to 3: 6 units right), which matches the blue arrow's length (from -3 to 3 is 6 units).
• $3 + (-6) = -3$: start at 3, move left 6 to -3, but the red arrow is not starting at 3.
• $3 + 6 = 9$: too far right.

So the correct operation is $-3 + 6$.

Answer:

-3 + 6 (the second option, so the answer is the option with -3 + 6, which is the second circle option: \(\boldsymbol{-3 + 6}\))