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

Explanation:

Step1: Recall absolute - value property

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

Step2: Analyze each equation

Equation 1: (|-x - 3|=5)

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

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

We can solve it as (2x-1 = 0), because the only way for the absolute - value to be (0) is when the expression inside the absolute - value is (0).

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

Since the left - hand side (|5 - 3x|\geq0) for all real (x) and the right - hand side is (-8\lt0), this equation has no solution.

Equation 4: (|-x + 9| = 0)

We can solve it as (-x + 9 = 0) because the absolute - value is (0).

Answer:

(|5 - 3x|=-8)