Question

Misha found that the equation -|2x-10|-1=2 had two possible solution x=3.5and x =-6.5. Which explains whether or not her solutions are correct

Answer 1

Answer:

She is not correct.

Step-by-step explanation:

Given : Misha found that the equation $- |2x-10|-1=2$  had two possible solution x=3.5 and x =-6.5.

To find : Explains whether or not her solutions are correct.

Solution :

The first thing we solve the equation to get solution,

$- |2x-10|-1=2$

Add 1 on both side of equation :

 $- |2x-10|-1+1=2+1$

 $- |2x-10|=3$

Multiply both sides of the equation by -1:

 $- |2x-10|(-1)=3(-1)$

 $|2x-10|=-3$

We observe that the result of the expression in absolute value is -3.

The result of an absolute value function is always greater than or equal to zero.

Which implies , the equation has no solution.

Therefore, Misha solutions were incorrect.

Answer 2

-|2x-10|-1=2 has NO solutions, because the absolute value function is never negative.  Can be 0, can be positive, but can NOT be negative.