Suzy was adding numbers on a number line. she started at –2 and then she added –3. she wrote that her answer was +5.
is suzy's answer reasonable?
a.
yes, it is reasonable because if you add two numbers, you will get a number that is greater than either of the two numbers.
b.
no, it is not reasonable because if you start at –2, you would move 3 places to the left and get –5.
c.
no, it is not reasonable because if you start at –2, you would move 3 places to the right and get +1.

First, what is Suzy doing?
She is adding (-3) to (-2)

Assume it on number line, go (-3) steps from (-2) that means we need to go 3 steps back from (-2)!
We land on (-5)!

Again, mathematically:
Suzy added (-2) and (-3)
(-2)+(-3) = - 2 - 3 = -5
But her answer is? (+5)
So, she's incorrect!
So, the answer is (B)

Well, let's think about what we're saying here. In mathematics, whenever a negative is added, it's the same as subtracting the positive of that number. For instance, if we had 5 + -9, that would be the same as saying 5 - 9.
So, let us put the equation we have into more common terms. Suzy started at -2, so that is our starting number. Then she added -3. Remember that adding negatives is the same thing as subtracting positives. So now, our expression looks like this:

-2 + -3

which is the same as

-2 - 3

When you subtract 3 from negative two, you are left with -5.

-2 - 3 = -5

We can see that -5 does not equal +5 (Suzy's resulting number), so we can automatically deselect any answer choices that say her logic is sound. Answer choice A is gone.
Let us examine the other choices and see which the right one would be.

B. No, it is not reasonable because if you start at -2, you would move 3 places to the left and get -5.

This choice sounds correct, since that is the result we ended up with, but let's take a look at the last answer anyway.

C. No, it is not reasonable because if you start at -2, you would move 3 places to the right and get +1.

This choice is incorrect. We didn't end up even close to +1, so this choice is not the correct answer choice.

We are left with choice B, which is our correct answer.
Hope that helped! =)