4) \( 7 . n-14=3 n+22 \)

To solve the equation \( 7n - 14 = 3n + 22 \), start by getting all terms involving \( n \) on one side of the equation. Subtract \( 3n \) from both sides to yield \( 7n - 3n - 14 = 22 \), which simplifies to \( 4n - 14 = 22 \). Next, add 14 to both sides resulting in \( 4n = 36 \). Finally, divide both sides by 4 to find \( n = 9 \). If you're tempted to make mistakes, remember to carefully manage your operations! It’s easy to overlook the need to balance the equation; always double-check your additions and subtractions. With practice, solving will become second nature, and checking your work will turn from a chore into a habit!