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(a) Finding the Other Integer When the Sum is Given

We know that the sum of two integers is \(\(-15\)\), and one of those integers is \(\(56\)\). Let the other integer be \(\(x\)\).

Given:
\(\[ 56 + x = -15 \]\)

To find \(\(x\)\), we need to isolate \(\(x\)\):

\(\[ x = -15 - 56 \]\)

Now, subtract \(\(56\)\) from \(\(-15\)\):

\(\[ x = -71 \]\)

So, the other integer is \(\(-71\)\).

### (b) Finding the Integer When the Difference is Given

We need to find an integer \(\(y\)\) such that the difference between \(\(y\)\) and \(\(-13\)\) is \(\(16\)\).

Given:
\(\[ y - (-13) = 16 \]\)

Simplify the left side:
\(\[ y + 13 = 16 \]\)

To isolate \(\(y\)\), we subtract \(\(13\)\) from both sides:

\(\[ y = 16 - 13 \]\)

Subtract \(\(13\)\) from \(\(16\)\):

\(\[ y = 3 \]\)

So, the integer is \(\(3\)\).

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