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? a. She is correct, because both solutions satisfy the equation. b. She is not correct, because she made a sign error. c. She is not correct, because there are no solutions. d. She is not correct, because there is only one solution: x = 3.5.

Answer 1

For this case we have the following expression:
 $- | 2x - 10 | - 1 = 2$
 The first thing we must do is rewrite the expression.
 For this, we follow the following steps:
 1) Add 1 on both sides of the equation:
 $- | 2x - 10 | - 1 + 1 = 2 + 1$
 $- | 2x - 10 | = 3$
 2) Multiply both sides of the equation by -1:
 $(-1) (- | 2x - 10 |) = (-1) (3)$
 $| 2x - 10 | = -3$
 We observe that the result of the expression in absolute value is -3.
 Therefore, the equation has no solution:
 The result of an absolute value function is always greater than or equal to zero.
 Answer:
 c. She is not correct, because there are no solutions.

Answer 2

$-|2x-10|-1=2 \ \ \ |+1 \\ -|2x-10|=3 \ \ \ |\times (-1) \\ |2x-10|=-3$

The absolute value of any number is greater than or equal to 0.
The equation has no solution.

The answer is C. She is not correct, because there are no solutions.