misha found that the equation -|2x - 10| - 1 = 2 had two possible solutions: x = 3.5 and x = -6.5. which…

misha found that the equation -|2x - 10| - 1 = 2 had two possible solutions: x = 3.5 and x = -6.5. which explains whether or not her solutions are correct? she is correct, because both solutions satisfy the equation. she is not correct, because she made a sign error. she is not correct, because there are no solutions. she is not correct, because there is only one solution: x = 3.5.

misha found that the equation -|2x - 10| - 1 = 2 had two possible solutions: x = 3.5 and x = -6.5. which explains whether or not her solutions are correct? she is correct, because both solutions satisfy the equation. she is not correct, because she made a sign error. she is not correct, because there are no solutions. she is not correct, because there is only one solution: x = 3.5.

Answer

Explanation:

Step1: Isolate the absolute - value expression

First, rewrite the given equation (-|2x - 10|-1 = 2). Add 1 to both sides of the equation: (-|2x - 10|=2 + 1), so (-|2x - 10|=3), and then (|2x - 10|=-3).

Step2: Analyze the absolute - value property

The absolute - value of any real number (a), denoted as (|a|), is defined as (|a|=\begin{cases}a, & a\geq0\-a, & a < 0\end{cases}), and (|a|\geq0) for all real numbers (a). Since the left - hand side (|2x - 10|\geq0) and the right - hand side is (-3<0), there are no real numbers (x) that satisfy the equation (|2x - 10|=-3).

Answer:

She is not correct, because there are no solutions.