Question

solve the absolute value equation or indicate that the equation has no solution.\\(|x + 4| + 3 = 1\\)\\(\dots\\)\\(\\)select the correct choice below and, if necessary, fill in the answer box to complete your choice\\(\\)\\(\bigcirc\\) a. the solution set is \\(\\{\square\\}\\)\\(\\) (use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)\\(\\)\\(\bigcirc\\) b. the solution set is the empty set.

Explanation:

Step1: Isolate the absolute value term

Subtract 3 from both sides.
$$|x+4| + 3 - 3 = 1 - 3$$
$$|x+4| = -2$$

Step2: Analyze absolute value validity

Absolute value cannot be negative.
No real number $x$ makes $|x+4|=-2$ true.

Answer:

B. The solution set is the empty set