Question

Which of the following expressions are equivalent?

Select all that apply.

A) 57 - 13 and 57 - (-13)

B) 31 - 8 and -31 + (-8)

C) 11 - (-5) and -5 + (-11)

D) -29 - (-6) and 6 + (-29)

Answer 1

After evaluating each expression pair, only option D (-29 - (-6) and 6 + (-29)) has equivalent expressions. Options A, B, and C do not yield the same result when simplified.

Step-by-step explanation:

Let's evaluate which of the following expressions are equivalent:

• A) 57 - 13 and 57 - (-13): The first expression is a simple subtraction, and the result is 44. The second expression involves subtracting a negative number, which is the same as adding its positive counterpart, so 57 + 13 is also 70. These expressions are not equivalent.
• B) 31 - 8 and -31 + (-8): The first expression results in 23, while the second expression results in the addition of two negative numbers, yielding -39. These are not equivalent.
• C) 11 - (-5) and -5 + (-11): Subtracting a negative number is equivalent to addition, so 11 - (-5) is the same as 11 + 5, which is 16. The second expression adds two negative numbers, resulting in -16. These expressions are not equivalent.
• D) -29 - (-6) and 6 + (-29): The first expression is the same as -29 + 6, which results in -23. The second expression also combines -29 and 6 but using addition, so the result is the same: -23. Therefore, these expressions are equivalent.

In conclusion, only option D has equivalent expressions.