Question

solve the absolute value equation or indicate that the equation has no solution.
|x| = 6

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}.
(use a comma to separate answers as needed.)
b. the solution is the empty set.

Explanation:

Step1: Recall absolute value definition

The absolute value of a number \( x \), denoted \( |x| \), is the distance of \( x \) from 0 on the number line. So, if \( |x| = a \) (where \( a\geq0 \)), then \( x = a \) or \( x = -a \).

Step2: Apply to the equation \( |x| = 6 \)

Using the definition, we have two cases:

• Case 1: \( x = 6 \) (since the distance from 6 to 0 is 6)
• Case 2: \( x = -6 \) (since the distance from -6 to 0 is also 6)

Answer:

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