Question

solve the absolute value inequality
|6x - 3| < 27

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. 6x - 3 <

b. -27 < 6x - 3 < 27

c. 6x - 3 < or 6x - 3 >

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
(simplify your answer.)
b. the solution set is ∅

Explanation:

Step1: Rewrite absolute value inequality

$$-27 < 6x - 3 < 27$$

Step2: Add 3 to all parts

$$-27 + 3 < 6x - 3 + 3 < 27 + 3$$
$$-24 < 6x < 30$$

Step3: Divide all parts by 6

$$\frac{-24}{6} < \frac{6x}{6} < \frac{30}{6}$$
$$-4 < x < 5$$

Step4: Convert to interval notation

Interval notation uses parentheses for strict inequalities, so the solution is $(-4, 5)$.

Answer:

First part (rewritten inequality): B. $-27 < 6x - 3 < 27$
Second part (interval notation): A. The solution set in interval notation is $(-4, 5)$