Question

which equation has no solution?
| - x - 3| = 5
|2x - 1| = 0
|5 - 3x| = - 8
| - x + 9| = 0

Explanation:

Step1: Recall absolute - value property

The absolute - value of a real number \(a\), denoted as \(|a|\), is always non - negative, i.e., \(|a|\geq0\) for all real numbers \(a\).

Step2: Analyze each equation

Equation \(|-x - 3| = 5\)

Since \(5\geq0\), we can solve it as \(-x - 3=5\) or \(-x - 3=-5\).

Equation \(|2x - 1| = 0\)

Since \(0\geq0\), we solve \(2x - 1 = 0\), which gives \(x=\frac{1}{2}\).

Equation \(|5 - 3x|=-8\)

Since \(-8\lt0\) and the absolute - value of any real number \(5 - 3x\) is non - negative, this equation has no solution.

Equation \(|-x + 9| = 0\)

Since \(0\geq0\), we solve \(-x + 9 = 0\), which gives \(x = 9\).

Answer:

\(|5 - 3x|=-8\)