Question

solve the absolute value equation.
|x - 6| + 8 = 9
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 absolute value term

Subtract 8 from both sides:
$|x-6| + 8 - 8 = 9 - 8$
$|x-6| = 1$

Step2: Split into two equations

For absolute value $|A|=B$, solve $A=B$ and $A=-B$:
$x-6 = 1$ and $x-6 = -1$

Step3: Solve first equation

Add 6 to both sides:
$x = 1 + 6$
$x = 7$

Step4: Solve second equation

Add 6 to both sides:
$x = -1 + 6$
$x = 5$

Answer:

A. The solution set is {5, 7}