Question

rewrite the inequality without absolute value bars. select the correct choice below and fill in the answer box(es) (simplify your answers.)
a. $4x - 2 < \square$ or $4x - 2 > \square$
b. $-14 < 4x - 2 < 14$
c. $4x - 2 < \square$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in interval notation is $\square$. (simplify your answer.)
b. the solution set is $\varnothing$.

Explanation:

To solve the inequality involving absolute value and find the solution set, we start with the rewritten inequality from option B: \(-14 < 4x - 2 < 14\).

Step 1: Add 2 to all parts of the inequality

To isolate the term with \(x\), we add 2 to each part of the compound inequality.
\[
-14 + 2 < 4x - 2 + 2 < 14 + 2
\]
Simplifying each part:
\[
-12 < 4x < 16
\]

Step 2: Divide all parts by 4

To solve for \(x\), we divide each part of the inequality by 4.
\[
\frac{-12}{4} < \frac{4x}{4} < \frac{16}{4}
\]
Simplifying each part:
\[
-3 < x < 4
\]

Step 3: Write the solution in interval notation

The interval notation for the solution set \(-3 < x < 4\) is \((-3, 4)\).

Answer:

A. The solution set in interval notation is \(\boxed{(-3, 4)}\)