Question

solve the absolute value equation or indicate that the equation has no solution.
|x - 4| = 8
select the correct choice below and, if necessary, fill in the answer box to complete your
a. the solution set is {}.
(simplify your answer. use a comma to separate answers as needed.)
b. the solution set is the empty set.

Explanation:

Step1: Recall absolute value definition

For \(|A| = B\) (where \(B\geq0\)), \(A = B\) or \(A=-B\). Here, \(A = x - 4\) and \(B = 8\) (which is \(\geq0\)). So we set up two equations:
\(x - 4 = 8\) or \(x - 4 = -8\)

Step2: Solve first equation

For \(x - 4 = 8\), add 4 to both sides:
\(x = 8 + 4 = 12\)

Step3: Solve second equation

For \(x - 4 = -8\), add 4 to both sides:
\(x = -8 + 4 = -4\)

Answer:

12, -4