To determine which expressions are equivalent to $-5 + 7 - (-3)$, we will simplify the given expression and compare it to the choices provided.

1. Simplify the given expression: $-5 + 7 - (-3)$ The expression includes a double negative, which means subtracting a negative number is the same as adding the positive value of that number. $-5 + 7 - (-3) = -5 + 7 + 3$

So the simplified expression is: $-5 + 7 + 3$

Now, let's compare this with each choice:

Choice A: $-5 + 7 + 3$

• This matches our simplified expression exactly.
• Therefore, this choice is correct.

Choice B: $-5 + 7 - 3$

• Simplifying this expression: $-5 + 7 - 3 = 2 - 3 = -1$
• This does not match the simplified expression $-5 + 7 + 3 = 5$.
• Therefore, this choice is incorrect.

Choice C: $-5 + (7 - 3)$

• Simplifying inside the parentheses first: $7 - 3 = 4$
• Substituting back into the expression: $-5 + 4 = -1$
• This does not match the simplified expression $-5 + 7 + 3 = 5$.
• Therefore, this choice is incorrect.

Choice D: $(-5 + 7) + 3$

• Simplifying inside the parentheses first: $-5 + 7 = 2$
• Substituting back into the expression: $2 + 3 = 5$
• This matches the simplified expression exactly.
• Therefore, this choice is correct.

So, the two correct answers are:

A. $-5 + 7 + 3$ D. $(-5 + 7) + 3$

Would you like any details or have any questions?

Here are some related questions to consider:

1. What is the result of simplifying $-8 + 10 - (-5)$?
2. How do you handle double negatives in mathematical expressions?
3. Can you simplify the expression $-4 + 9 - (-2)$?
4. What are the steps to solve $(-7 + 3) + 4$?
5. How does the order of operations affect expressions with parentheses and negative numbers?

Tip: Always remember that subtracting a negative number is equivalent to adding the positive value of that number.