Final answer:
To solve the equation 2|x-9|=20, isolate the absolute value expression and consider two cases: when x-9 is positive and when it is negative. The solutions are x=19 and x=-1, and their sum is 18.
Step-by-step explanation:
To solve the equation 2|x-9|=20, you need to isolate the absolute value expression. Begin by dividing both sides of the equation by 2 to get |x-9|=10. Then, consider two cases: x-9 could be either positive or negative when the absolute value is equal to 10.
If x-9 is positive, then x-9=10. Solving for x, we have x=19.
If x-9 is negative, then -(x-9)=10. Solving for x, we have x=-1.
The sum of the solutions is 19 + (-1) = 18.