To add the expression \((2m - 3) + (3n - 1) + (3m + 1)\), we can group like terms together.
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Combine the \(m\) terms:
- From \(2m\) and \(3m\): \(2m + 3m = 5m\)
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Combine the \(n\) terms:
- The only \(n\) term is \(3n\): \(3n\)
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Combine the constant terms:
- From \(-3\), \(-1\), and \(1\): \(-3 - 1 + 1 = -3\)
Now, putting it all together, we have:
\[ 5m + 3n - 3 \]
Therefore, the sum of the expression \((2m - 3) + (3n - 1) + (3m + 1)\) is:
\[ 5m + 3n - 3 \]