We are tasked with finding expressions that are equivalent to the following expression:

$6 + (-4) - 5$

First, let's simplify $6 + (-4) - 5$:

$6 + (-4) = 6 - 4 = 2$ $2 - 5 = -3$

So, the expression simplifies to $-3$. Now, let's check the given choices one by one to see which ones also simplify to $-3$.

Choice A: $6 - 4 - (-5)$

This simplifies as follows: $6 - 4 - (-5) = 6 - 4 + 5 = 2 + 5 = 7$ This does not equal $-3$.

Choice B: $6 + 4 - 5$

This simplifies as follows: $6 + 4 - 5 = 10 - 5 = 5$ This does not equal $-3$.

Choice C: $-5 + 6 - 4$

This simplifies as follows: $-5 + 6 = 1$ $1 - 4 = -3$ This equals $-3$, so it is equivalent.

Choice D: $-4 + (-5) + 6$

This simplifies as follows: $-4 + (-5) = -9$ $-9 + 6 = -3$ This also equals $-3$, so it is equivalent.

Conclusion:

The two expressions that are equivalent to $6 + (-4) - 5$ are Choice C and Choice D.

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Would you like further clarification or additional details?

Here are 5 related questions:

1. What is the difference between subtracting a negative number and subtracting a positive number?
2. How can you simplify expressions involving both addition and subtraction of integers?
3. How does the order of operations affect the evaluation of arithmetic expressions?
4. Can you simplify expressions involving more than two terms, like $6 + (-4) + (-5)$?
5. How do you handle multiple negative signs in an expression?

Tip:

When simplifying arithmetic expressions, always start by performing operations within parentheses and follow the order of operations (PEMDAS/BODMAS).