Use indirect reasoning to show that there is no whole number, \( n \), which solves the equation \( 4 n+14=41 \). Is the number 41 even or odd? odd even Is the number 14 even or odd? odd Is the number \( 4 n \) even or odd? odd even is the sum \( 4 n+14 \) even or odd? odd even

1. Assume there exists a whole number \( n \) such that \[ 4n + 14 = 41. \] 2. Notice that \(41\) is an odd number. 3. The number \(14\) is even. 4. For any whole number \( n \), the product \(4n\) is even (because \(4\) is even and the product of an even number with any whole number is even). 5. The sum of two even numbers is even; therefore, the left-hand side, \(4n + 14\), must be even. 6. We now have that \(4n + 14\) is even while the right-hand side is odd. This is a contradiction, since an even number cannot equal an odd number. 7. Thus, by indirect reasoning (proof by contradiction), there is no whole number \( n \) that satisfies the equation. - The number \(41\) is odd. - The number \(14\) is even. - The term \(4n\) is even. - The sum \(4n + 14\) is even.