Question

solve the following absolute value equation.

\\-3|x - 1| + 6 = -9\\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution set is \\(\\{\quad\\}\\).
(simplify your answer. use a comma to separate answers as needed.)

b. the solution set is \\(\\{\\}\\) or \\(\varnothing\\).

Explanation:

⚡ Using what you learned: Solving Absolute Value Equations

Step 1: Isolate the absolute value expression

$$ -3|x - 1| + 6 = -9 $$

Subtract \(6\) from both sides:

$$ -3|x - 1| = -15 $$

Divide both sides by \(-3\):

$$ |x - 1| = 5 $$

Step 2: Split into two cases

Since \(|x - 1| = 5\), the expression inside the absolute value can be either \(5\) or \(-5\):

Case 1:

$$ x - 1 = 5 $$

$$ x = 6 $$

Case 2:

$$ x - 1 = -5 $$

$$ x = -4 $$

Answer:

A. The solution set is \(\{6, -4\}\).