The problem shows a sequence of equations, and you are asked to identify the mathematical property that justifies the step from one line to the next. Here's how the justification for each step works:

From Line 1 to Line 2:

• Line 1: $(-10 + 9x) + 2$
• Line 2: $(9x + (-10)) + 2$

This is an example of the Commutative Property of Addition, which states that you can change the order of terms in an addition expression. Here, the terms $-10$ and $9x$ are swapped.

From Line 2 to Line 3:

• Line 2: $(9x + (-10)) + 2$
• Line 3: $9x + (-10 + 2)$

This step applies the Associative Property of Addition, which allows you to regroup terms without changing the result. The parentheses around $9x$ and $-10$ are removed, and instead, $-10$ is grouped with $2$.

From Line 3 to Line 4:

• Line 3: $9x + (-10 + 2)$
• Line 4: $9x + (-8)$

This step involves Simplification by performing the arithmetic inside the parentheses. $-10 + 2 = -8$, so the expression simplifies to $9x + (-8)$.

Would you like further clarification or additional details?

Here are some related questions to expand your understanding:

1. What is the difference between the commutative and associative properties of addition?
2. Can the distributive property be applied to similar problems, and how?
3. How does the commutative property apply in multiplication?
4. Why is simplifying expressions an important step in solving equations?
5. In what situations would you use the associative property over other properties?

Tip: Always look for properties like commutative and associative to reorganize and simplify expressions easily.