Question

solve the absolute value inequality
|4x - 2| < 14

rewrite the inequality without absolute value bars. select the correct choice below and fill in the answer box(es) to complete your choice.
(simplify your answers.)

a. 4x - 2 < □ or 4x - 2 > □

b. □ < 4x - 2 < □

c. 4x - 2 < □

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). Here, \(a = 4x - 2\) and \(b = 14\). So the correct form is \( - 14<4x - 2<14\). So the correct option is B.

Step2: Fill in the boxes

Using the rule, the left box is \(-14\) and the right box is \(14\).

Answer:

B. \(-14 < 4x - 2 < 14\)