To solve the expression \((4x + 2) + (2x + 3) \mod 5\), we first combine the terms:
\[ (4x + 2) + (2x + 3) = 4x + 2 + 2x + 3 = (4x + 2x) + (2 + 3) = 6x + 5 \]
Next, we reduce the polynomial \(6x + 5\) modulo 5.
First, we evaluate each term mod 5:
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\(6x \mod 5\): \[ 6 \mod 5 = 1 \quad \text{(since } 6 - 5 = 1\text{)} \] Thus, \(6x \mod 5 = 1x \mod 5 = x\).
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\(5 \mod 5 = 0\): \[ 5 - 5 = 0 \]
Now, putting it all together:
\[ (6x + 5) \mod 5 = (x + 0) \mod 5 = x \]
Therefore, the simplified expression is:
\[ \boxed{x} \]