Question

Solve (4x + 2) + (2x + 3) ( mod 5 )

Answer 1

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:

1. \(6x \mod 5\):
\[
6 \mod 5 = 1 \quad \text{(since } 6 - 5 = 1\text{)}
\]
Thus, \(6x \mod 5 = 1x \mod 5 = x\).

2. \(5 \mod 5 = 0\):
\[
5 - 5 = 0
\]

Now, putting it all together:

\[
(6x + 5) \mod 5 = (x + 0) \mod 5 = x
\]

Therefore, the simplified expression is:

\[
\boxed{x}
\]