The absolute value of the sum of two different integers with the same sign is 8. Pat says there are three pairs of integers that match this description. Do you agree? Explain.

No. There are 6 pairs of such integers

Step-by-step explanation:

The absolute value of the sum of two different integers with the same sign is 8. This means either two positive or negative integers are added to give an absolute value of 8.

According to Pat there are only 3 possibilities, when infact there are more than 3 such possibilities. All the possibilities are listed below:

1 + 7 = 8

2 + 6 = 8

3 + 5 = 8

Pat might have considered only these 3 possibilities, ignoring the next combinations of negative numbers:

-1 + (-7) = - 1 - 7 = - 8 Absolute value of - 8 = | - 8 | = 8

-2 + (-6) = - 2 - 6 = - 8

-3 + (-5) = - 3 - 5 = - 8

Therefore, there are total 6 pairs of integers that match the description. The positive and negative integers should not be counted as the same.