consider the two expressions: -3 - (-11) and -3 + 11. which statement correctly explains why these two expressions are or not equivalent.
a. they are not equivalent because subtracting -11 is not the same as adding +11.
b. They are not equivalent because they do not get the same answer.
c. They are equivalent because the numerals are the same.
d. They are equivalent because to subtract integers you can add the opposite of the number that is being subtracted.
d. They are equivalent because to subtract integers you can add the opposite of the number that is being subtracted.
d. They are equivalent because to subtract integers you can add the opposite of the number that is being subtracted.
The correct statement that explains why these two expressions are or not equivalent is option A: "They are not equivalent because subtracting -11 is not the same as adding +11."
To understand why this is the case, we need to understand the rules of subtracting and adding integers.
In the expression -3 - (-11), we have a subtraction of a negative number. According to the rules of subtracting integers, subtracting a negative number is the same as adding its opposite. So, -3 - (-11) can be rewritten as -3 + 11.
On the other hand, in the expression -3 + 11, we have a simple addition of -3 and 11.
While the values of the numerals in both expressions are the same, the actual operations being performed are different. Subtraction and addition are not interchangeable. Thus, these expressions are not equivalent.
Therefore, option A correctly explains that these two expressions are not equivalent because subtracting -11 is not the same as adding +11.