classify each statement as sometimes, always, or never true. give examples or properties to support your answer d+ (-d)=0

What is your answer?

To classify the statement "d + (-d) = 0" as sometimes, always, or never true, we can establish its properties and verify if these properties hold true for any given value of 'd.'

In this case, let's start with understanding the operations involved:

1. '+' denotes addition.
2. '-d' represents the additive inverse of 'd.' It is the value that, when added to 'd,' results in zero.

Now, let's evaluate the statement for different values of 'd' and check if it holds true.

1. Sometimes True:
If 'd' represents any non-zero real number, then the statement "d + (-d) = 0" is sometimes true. This is because for any real number 'd,' the additive inverse '-d' exists such that when they are added, it results in zero.

Example:
For d = 5, -d = -5
5 + (-5) = 0

2. Always True:
If 'd' represents zero, then the statement "d + (-d) = 0" is always true. Since the additive inverse of zero is also zero, adding zero to its additive inverse will always give zero.

Example:
For d = 0,
0 + (-0) = 0

Therefore, the statement "d + (-d) = 0" is always true when d = 0 and sometimes true for any non-zero real number.

It is important to note that these classifications are based on the properties of addition and additive inverses in mathematics.