Answer:
x = 4
Explanation:
If |x-2| = |x-6|, then either (x-2) = (x-6) or (x-2) = -(x-6).
Simplifying the first equation, we get:
x - 2 = x - 6
Subtracting x from both sides, we get:
-2 = -6
This equation is not true for any value of x. Therefore, we need to consider the second equation:
x - 2 = -(x - 6)
Expanding the right-hand side, we get:
x - 2 = -x + 6
Adding x to both sides, we get:
2x - 2 = 6
Adding 2 to both sides, we get:
2x = 8
Dividing by 2, we get:
x = 4
Therefore, the solution to the equation |x-2| = |x-6| is x = 4.
We can check our solution by plugging in x = 4 into both sides of the equation:
|x-2| = |4-2| = 2
|x-6| = |4-6| = 2
Therefore, both sides of the equation are equal, which confirms our solution.
Therefore, x = 4 is the solution to the equation |x-2| = |x-6|.