### (a) Finding the Other Integer When the Sum is Given
We know that the sum of two integers is [tex]\(-15\)[/tex], and one of those integers is [tex]\(56\)[/tex]. Let the other integer be [tex]\(x\)[/tex].
Given:
[tex]\[ 56 + x = -15 \][/tex]
To find [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex]:
[tex]\[ x = -15 - 56 \][/tex]
Now, subtract [tex]\(56\)[/tex] from [tex]\(-15\)[/tex]:
[tex]\[ x = -71 \][/tex]
So, the other integer is [tex]\(-71\)[/tex].
### (b) Finding the Integer When the Difference is Given
We need to find an integer [tex]\(y\)[/tex] such that the difference between [tex]\(y\)[/tex] and [tex]\(-13\)[/tex] is [tex]\(16\)[/tex].
Given:
[tex]\[ y - (-13) = 16 \][/tex]
Simplify the left side:
[tex]\[ y + 13 = 16 \][/tex]
To isolate [tex]\(y\)[/tex], we subtract [tex]\(13\)[/tex] from both sides:
[tex]\[ y = 16 - 13 \][/tex]
Subtract [tex]\(13\)[/tex] from [tex]\(16\)[/tex]:
[tex]\[ y = 3 \][/tex]
So, the integer is [tex]\(3\)[/tex].
