The expression "x - y + z" can be simplified and rearranged using the associative property and commutative property of addition. Let's break it down step by step:
1. x - y + z
According to the associative property of addition, the grouping of terms does not affect the result when only addition and subtraction are involved. Therefore, we can choose to group "y" and "z" together:
2. x + (-y + z)
Next, using the commutative property of addition, we can rearrange the terms "-y + z" as "z + (-y)":
3. x + (z + (-y))
Now, we have the expression "x + (z + (-y))". According to the associative property of addition, we can group "x" and "z + (-y)" together:
4. (x + z) + (-y)
Finally, we can rewrite the expression as "(x + z) - y", which is equivalent to "(x - y) + z":
5. (x + z) + (-y) = (x - y) + z
Therefore, "x - y + z" is indeed the same as both "x - (y + z)" and "(x - y) + z" due to the associative and commutative properties of addition.