When is absolute value of (x-4) is equal to 4-x?

When x \leq 4.

answer is given x less than or equal 4, x< = 4

I just forgot the x = 4 part, fixed.

please explain process

When does (x - 4) become negative?

absolute value of (x-4) becomes negative when the whole term is less than zero. I don’t get the x-4 = 0 part

The “absolute value” is never less than 0. The question is asking when does |x - 4| = 4 - x. Notice that when x \geq 4, x - 4 is positive and hence |x - 4| = x - 4. When x \leq 4, x - 4 is nonpositive and hence |x - 4| = 4 - x, because that’s when 4 - x is nonnegative.