To add the expressions \( (2m - 3) + (3n - 1) + (3m + 1) \), we will combine the like terms.
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Group the terms involving \( m \):
- \( 2m + 3m = 5m \)
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Group the terms involving \( n \):
- \( 3n \) (there's only one term with \( n \))
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Group the constant terms:
- \( -3 - 1 + 1 = -3\)
Now, combining everything together, we have:
\[ 5m + 3n - 3 \]
So, the final simplified expression is:
\[ 5m + 3n - 3 \]