Answer:
There are no extraneous solutions.
7 and -9 are the valid solutions
Explanation:
Given:
To find :
Solution:
Isolate the absolute value.


Divide both sides by -10.


The absolute value of an expression is its distance from zero.
It has two solutions, one negative and one positive.
The negative solution is:

Solving for k, we get:


The positive solution is:

Solving for k, we get:


We need to check both solutions to make sure they are not extraneous.
An extraneous solution is a solution that makes the original equation undefined.
Now that we have two potential solutions, k = 7 and k = -9, let's check them in the original equation to see if they are extraneous:
For k = 7:




For k = -9:





Both solutions, k = 7 and k = -9, satisfy the original equation, so there are no extraneous solutions.
7 and -9 are the valid solutions to the equation.