Question

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 1

She is not correct, because there are no solutions.

Reason:
-|2x − 10| − 1 = 2 implies −|2x − 10| = 3, so |2x − 10| = −3, which is impossible (absolute value is ≥ 0).
Also, plugging in Misha’s values gives −|2(3.5)−10|−1 = −4 and −|2(−6.5)−10|−1 = −14, neither equals 2.