which equation has no solution?\n|4x - 2| = -6\n|-2 - x| = 9\n|3x + 6| = 6\n|-2x + 8| = 0

Explanation:

Step1: Recall absolute - value property

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

Step2: Analyze each equation

Equation 1: (|4x - 2|=-6)

Since the left - hand side (|4x - 2|) is an absolute - value expression and must be non - negative ((|4x - 2|\geq0)), and the right - hand side is (-6\lt0), this equation has no solution.

Equation 2: (|-2 - x| = 9)

We can rewrite it as two equations: (-2 - x=9) or (-2 - x=-9). Solving (-2 - x = 9) gives (x=-11), and solving (-2 - x=-9) gives (x = 7).

Equation 3: (|3x + 6| = 6)

We can rewrite it as two equations: (3x+6 = 6) or (3x + 6=-6). Solving (3x+6 = 6) gives (x = 0), and solving (3x + 6=-6) gives (x=-4).

Equation 4: (|-2x + 8| = 0)

The equation (|-2x + 8| = 0) is equivalent to (-2x+8 = 0). Solving for (x) gives (x = 4).

Answer:

(|4x - 2|=-6)