write the following absolute value expressions as piecewise expressions:

y= abs(2x-4)

well, maybe it has something to do with

If x<2
then y = -(2x-4)
but
If x≥2
then y = 2x-4

To write the absolute value expression |2x-4| as a piecewise expression, you'll need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (2x-4) ≥ 0
If 2x-4 is greater than or equal to zero, then the absolute value expression simplifies to itself.
y = 2x-4

Case 2: (2x-4) < 0
If 2x-4 is less than zero, then the sign inside the absolute value changes.
To find the value of y in this case, we can negate the expression itself.
y = -(2x-4)
= -2x + 4

Combining the two cases, we have the piecewise expression for y = |2x-4|:

y =
2x-4 if 2x-4 ≥ 0
-2x+4 if 2x-4 < 0