Question

solve the absolute value equation.
|8v - 6| = -3

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: Recall absolute value property

The absolute value of a number, denoted as \(|x|\), is always non - negative. That is, for any real number \(x\), \(|x|\geq0\).

Step2: Analyze the given equation

We are given the equation \(|8v - 6|=-3\). But from the property of absolute value, the left - hand side \(|8v - 6|\) is always greater than or equal to \(0\) for all real numbers \(v\), and the right - hand side is \(- 3\) which is negative. Since a non - negative number can never be equal to a negative number, there are no real solutions for \(v\) that satisfy the equation.

Answer:

B. The solution set is \(\varnothing\).