Question

solve the absolute value equation.
|9n + 4| + 11 = 8
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}.
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. the solution set is ∅.

Explanation:

Step1: Isolate the absolute value term

Subtract 11 from both sides.
$$|9n + 4| + 11 - 11 = 8 - 11$$
$$|9n + 4| = -3$$

Step2: Analyze the absolute value result

The absolute value of any real expression is non-negative (≥ 0), so it cannot equal a negative number. No real number $n$ satisfies this equation.

Answer:

B. The solution set is $\emptyset$.