Question

which inequality is equivalent to |x - 4| < 9?
-9 > x - 4 < 9
-9 < x - 4 < 9
x - 4 < -9 or x - 4 < 9
x - 4 > -9 or x - 4 < 9

Explanation:

Step1: Recall absolute - value inequality rule

For \(|a|\lt b\) (\(b>0\)), it is equivalent to \(-b < a < b\). Here \(a=x - 4\) and \(b = 9\).

Step2: Apply the rule

Substituting \(a=x - 4\) and \(b = 9\) into \(-b < a < b\), we get \(-9

Answer:

B. \(-9 < x - 4 < 9\)