Use indirect reasoning to show that there is no whole number, \( n \), which solves the equation \( 6 n+14=31 \). odd Is the number 6 n even or odd? odd is the sum \( 6 n+14 \) even or odd? even Based on the above answers, why is there no whole number, \( n \), that solves the equation \( 6 n+14=31 \) ? A. Both sides of the equation are always odd. B. Both sides of the equation are always even. C. The left side of the equation is always even and the right side is always odd. D. The right side of the equation is always even and the left side is always odd. Theretore, \( n \) cannot be a whole number. (

The key to solving the equation \(6n + 14 = 31\) lies in the parity of both sides. We know that \(6n\) is even since any whole number multiplied by 6 is even. When we add 14 (which is also even), the entire left-hand side remains even. On the other side, 31 is an odd number. Since an even number can never equal an odd number, we conclude that there is no whole number \(n\) that satisfies the equation. Thus, the correct reasoning is that the left side \(6n + 14\) is always even, while the right side \(31\) is odd, confirming that we can't have a solution where both sides are equal. Hence, option C is correct: "The left side of the equation is always even and the right side is always odd."