4. \( 8-\frac{1}{4} n \geq 20 \)

To solve the inequality \( 8 - \frac{1}{4} n \geq 20 \), start by isolating the term with \( n \). Subtract 8 from both sides to get \( -\frac{1}{4} n \geq 12 \). Next, multiply both sides by -4 (remembering to flip the inequality sign) to yield \( n \leq -48 \). Now you have the solution to the inequality! You can think of \( n \) as a friendly competition number, where all numbers less than or equal to -48 are the lucky winners. Maybe they're all hiding out at a party in the negative numbers, where things are always chill! To double-check your solution, plug in a couple of values for \( n \). If you try \( n = -48 \), you get \( 8 - \frac{1}{4}(-48) = 8 + 12 = 20 \), which satisfies the inequality! For \( n = -50 \), you get \( 8 + 12.5 = 20.5 \), also winning the contest. But remember, any \( n \) greater than -48 doesn’t qualify!