Question

solve the absolute value inequality. complete parts a) through d).

\\|6x + 1| < 7\\

a) if necessary, write the inequality in standard form. select the correct choice and, if necessary, fill in the answer boxes to complete your choice.

a. the absolute value inequality \\(|6x + 1| < 7\\) is not in standard form, but can be written in standard form as \\(\square < \square\\).
(simplify your answers.)

b. the absolute value inequality \\(|6x + 1| < 7\\) is already in standard form.

Explanation:

Rewrite the absolute value inequality

$$ |6x + 1| < 7 \iff -7 < 6x + 1 < 7 $$

Identify standard form

The inequality is already in the standard form \(|ax + b| < c\) where the absolute value expression is isolated on one side.

Answer:

• (A) The absolute value inequality \(|6x + 1| < 7\) is not in standard form, but can be written in standard form as <blank></blank> < <blank></blank>
• (B) The absolute value inequality \(|6x + 1| < 7\) is already in standard form. (Correct answer)