Homework help

[Amalia78]

. Hosni gave the following argument that -(a + b) = -a + -b, for all integers a and b. If the argument is
correct, supply the missing reasons. If it is incorrect, explain why not.

This is what I have, so I am assuming the statement is true, however I am not sure about the missing reasons, can someone help explain.

- (a + b) = (-1) (a + b)
= (-1) a + (-1) b
= -a + -b

 

[chrisr]

You have written the symbolic (algebraic) expansion.

What you are most likely being asked to state is the answer to

"Why is the negative of the sum of two integers equal to the addition of the negatives of those two integers?"
if that is the case, state why or if that is not the case, state why.

a and b themselves could be negative or positive.

"Adding" two negative values could occur if we want to find the average of -10 and -4 degrees.
The average is halfway between them, which is -7, which is also the sum of both values divided by 2.
Since -7 is -14/2, then (-10 + -4)/2 is -14/2, hence -10 + -4 is -(10 + 4).

You can reason along those lines.