Question

which of the following is equivalent to |x - 1| < 5?
○ x - 1 < 5
○ 5 < x - 1 < 5
○ -5 < x - 1 < 5
○ -5 > x - 1 < 5

Explanation:

Step1: Recall absolute - value inequality rule

For \(|a|\lt b\) where \(b>0\), it is equivalent to \(-b < a < b\). Here \(a=x - 1\) and \(b = 5\).

Step2: Apply the rule

Substituting \(a=x - 1\) and \(b = 5\) into the rule, we get \(-5

Answer:

C. \(-5