**Which of the following expressions are equivalent to \[-5+7-(-3)\]?**

Choose 2 answers:

Choose 2 answers:

(Choice A)

\[-5+7+3\]

A

\[-5+7+3\]

(Choice B)

\[-5+7-3\]

B

\[-5+7-3\]

(Choice C)

\[-5+(7-3)\]

C

\[-5+(7-3)\]

(Choice D)

\[(-5+7)+3\]

D

\[(-5+7)+3\]

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.

Which of the following expressions are equivalent to [-5 + 7 - (-3)]? Choose 2 answers: (A) [-5 + 7 + 3], (B) [-5 + 7 - 3], (C) [-5 + (7 - 3)], (D) [(-5 + 7) + 3]

Explore how to simplify the expression [-5 + 7 - (-3)] and identify equivalent expressions. This problem focuses on integer operations, simplifying algebraic expressions, and handling double negatives. Suitable for students in Grades 6-8.

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