Question

solve each compound inequality and graph i

1. $\frac{n}{5} geq 1$ or $\frac{n}{6} leq 0$

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Explanation:

Step1: Solve \(\frac{n}{5} \geq 1\)

Multiply both sides by 5: \(n \geq 5\times1\)
\(n \geq 5\)

Step2: Solve \(\frac{n}{6} \leq 0\)

Multiply both sides by 6: \(n \leq 0\times6\)
\(n \leq 0\)

Step3: Combine the solutions

The compound inequality is "or", so we combine the two solution sets: \(n \leq 0\) or \(n \geq 5\)

Answer:

The solution to the compound inequality \(\frac{n}{5} \geq 1\) or \(\frac{n}{6} \leq 0\) is \(n \leq 0\) or \(n \geq 5\)