To solve this problem, we need to follow the object's movements step-by-step and determine its final position on the number line. Let's break down the movements one at a time:
1. The initial position of the object is at 0 on the number line.
2. The object first moves 3 units to the right:
[tex]\[
\text{Position after 1st move} = 0 + 3 = 3
\][/tex]
So, the object is now at position 3.
3. Next, the object moves 4 units to the left:
[tex]\[
\text{Position after 2nd move} = 3 - 4 = -1
\][/tex]
Now, the object is at position -1.
4. Finally, the object moves 6 units to the right:
[tex]\[
\text{Position after 3rd move} = -1 + 6 = 5
\][/tex]
So, the object ends up at position 5.
The displacement of the object is its final position relative to its initial position. Therefore, after all the movements, the displacement of the object is [tex]\(5\)[/tex] units.
