Solve the equation.
2|x-8|=4
Select the correct choice and, if necessary, fill in the answer box in your choice below.
x=
There is no solution.
To solve the equation 2|x-8|=4, we can start by dividing both sides of the equation by 2:
|x-8| = 2
Now, we can consider two cases:
Case 1: (x-8) is positive:
If (x-8) is positive, then |x-8| is equal to (x-8).
So, the equation becomes:
x-8 = 2
Now, we can solve for x:
x = 2 + 8
x = 10
Case 2: (x-8) is negative:
If (x-8) is negative, then |x-8| is equal to -(x-8).
So, the equation becomes:
-(x-8) = 2
Now, we can solve for x:
-x + 8 = 2
x - 8 = -2
x = -2 + 8
x = 6
Therefore, the equation has two solutions: x = 10 and x = 6.