Question

which compound inequality can be used to solve the inequality |3x + 2|>7? -7 < 3x + 2 > 7 -7 > 3x + 2 > 7 3x + 2 > -7 or 3x + 2 > 7 3x + 2 < -7 or 3x + 2 > 7

Explanation:

Step1: Recall absolute - value inequality rule

For \(|a|>b\) (\(b > 0\)), it is equivalent to \(a < - b\) or \(a>b\).

Step2: Identify \(a\) and \(b\) in the given inequality

In \(|3x + 2|>7\), \(a = 3x+2\) and \(b = 7\).

Step3: Apply the rule

By the rule, \(3x + 2<-7\) or \(3x + 2>7\).

Answer:

\(3x + 2 < - 7\) or \(3x + 2>7\)