Final answer:
The expressions equivalent to (−5)−(−12) are (−5)+12 and 7. Therefore, the correct options are B and E, with C being contextually correct depending on interpretation.
Step-by-step explanation:
The question asks to select all the options that are equivalent to (−5)−(−12). To find the equivalent expressions, we need to understand how subtraction and addition of negative numbers work. When subtracting a negative from a negative, it is equivalent to addition. Therefore, (−5)−(−12) is the same as (−5)+12.
- A. -7: This is incorrect because (−5)+12 equals 7, not -7.
- B. 7: This is correct. (−5)+12 results in 7.
- C. The difference between -5 and -12: This is correct in context because the expression (−5)−(−12) represents the difference; however, typically the "difference" implies subtracting the second number from the first, which could lead to confusion.
- D. The difference between -12 and -5: This is incorrect. This phrasing suggests -12 - (−5), which would result in -7, not 7.
- E. (−5)+12: This is correct since it is another way to express (−5)−(−12).
- F. (−5)+(−12): This is incorrect. This adds two negative numbers, resulting in -17, not 7.
Therefore, the correct answers are options B and E, and possibly C depending on interpretation.