Question

Carlos is using a number line to add another integer to –4. He begins by showing –4 on the number line, as shown below. Carlos adds the other integer on the number line and says that the sum is negative. A number line going from negative 5 to positive 5. The area between negative 4 to 0 is highlighted.

Answer 1

Answer:

I suppose that you want to find the possible values of the integer that Carlos add to -4.

The initial number is -4

Then we add another integer K,

-4 + K = N

And we know that N < 0.

Then we have:

-4 + K < 0

K < 4.

Now we know the possible values of the integer K.

But we also know that the highlighted area is the region [-4, 0]

Then we also have the restriction:

-4 < -4 + K < 0

Then the possible values of K are given by.

-4 + 4 < K < 0 + 4

0 < K < 4

And K is integer, so the possible values of K are:

{1, 2, 3}