Question

solve for s.
4|s - 1| > 80
write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. use fractions, or improper fractions in simplest form.

Explanation:

Step1: Divide both sides by 4

To isolate the absolute value expression, we divide both sides of the inequality \(4|s - 1|>80\) by 4.
\(\frac{4|s - 1|}{4}>\frac{80}{4}\)
Simplifying, we get \(|s - 1|>20\)

Step2: Solve the absolute value inequality

The absolute value inequality \(|s - 1|>20\) means that \(s - 1\) is either less than - 20 or greater than 20. So we have two cases:
Case 1: \(s - 1<-20\)
Adding 1 to both sides, we get \(s<-20 + 1=-19\)
Case 2: \(s - 1>20\)
Adding 1 to both sides, we get \(s>20 + 1 = 21\)

Answer:

\(s < - 19\) or \(s>21\)