Question

describe the graph of the solution set of |2x - 2| > 24.

Explanation:

Step1: Solve the absolute - value inequality

For an absolute - value inequality \(|A|>B\) (where \(B > 0\)), the solution is \(A > B\) or \(A<-B\).
Given the inequality \(|2x - 2|>24\), we can split it into two separate inequalities:
\(2x-2>24\) or \(2x - 2<-24\)

Step2: Solve \(2x-2>24\)

Add 2 to both sides of the inequality:
\(2x-2 + 2>24 + 2\)
\(2x>26\)
Divide both sides by 2:
\(x > 13\)

Step3: Solve \(2x - 2<-24\)

Add 2 to both sides of the inequality:
\(2x-2 + 2<-24 + 2\)
\(2x<-22\)
Divide both sides by 2:
\(x<-11\)

Step4: Describe the graph

The solution set is \(x < - 11\) or \(x>13\). On the number line, the graph will consist of two rays. One ray starts at \(-11\) (with an open circle, since \(x=-11\) does not satisfy the inequality) and extends to the left (towards negative infinity). The other ray starts at \(13\) (with an open circle, since \(x = 13\) does not satisfy the inequality) and extends to the right (towards positive infinity).

Answer:

The graph of the solution set \(x < - 11\) or \(x>13\) consists of two open - ray graphs: one to the left of \(-11\) (open circle at \(-11\)) and one to the right of \(13\) (open circle at \(13\)).