Question

solve the following absolute value equation.

\\-6|x - 5| + 9 = -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 term

$$ -6|x - 5| + 9 = -9 $$

$$ -6|x - 5| = -18 $$

$$ |x - 5| = 3 $$

Step 2: Split into two cases

$$ x - 5 = 3 \quad \text{or} \quad x - 5 = -3 $$

Step 3: Solve for x

$$ x = 8 \quad \text{or} \quad x = 2 $$

Answer:

A. The solution set is {2, 8}.