Question

1. solve and state the solution in set notation if possible.

|4x - 8| = -1

Explanation:

Step1: Recall absolute value property

The absolute value of a number, denoted as \(|a|\), is always non - negative, i.e., \(|a|\geq0\) for any real number \(a\). In the equation \(|4x - 8|=-1\), the left - hand side \(|4x - 8|\) represents the absolute value of the expression \(4x - 8\). Since the absolute value of any real number is greater than or equal to \(0\), and the right - hand side of the equation is \(- 1\) (which is negative), there is no real number \(x\) that can satisfy this equation.

Answer:

The solution set is \(\varnothing\) (the empty set) because the absolute value of an expression cannot be negative.