Question

find the solution to |3x| > 4. (1 point)
(-∞, -4/3 ∪ 4/3, ∞)
-4/3, 4/3
(-∞, -4/3) ∪ (4/3, ∞)
(-4/3, 4/3)

Explanation:

Step1: Recall absolute - value inequality rule

For \(|a|>b\) (\(b > 0\)), it is equivalent to \(a>b\) or \(a < - b\). Here \(a = 3x\) and \(b = 4\), so \(3x>4\) or \(3x<-4\).

Step2: Solve \(3x>4\)

Divide both sides of the inequality \(3x>4\) by 3. We get \(x>\frac{4}{3}\).

Step3: Solve \(3x < - 4\)

Divide both sides of the inequality \(3x < - 4\) by 3. We get \(x<-\frac{4}{3}\).

Answer:

C. \((-\infty,-\frac{4}{3})\cup(\frac{4}{3},\infty)\)