3- l2x-4l is less than or equal to 1

are the values of x

x is greater than or equal to 3
x is less than or equal to -3

3 - |2x-4| </= 1

-|2x-4| </= -2
then
|2x-4| >/= 2
so
(2x-4) >/= 2

2 x >/= 6

x >/ = 3
OR
-(2x-4) >/= 2
2x-4 </= -2
2 x </= 2
x </= 1

To find the values of x that satisfy the inequality 3 - |2x - 4| ≤ 1, we need to consider two cases: when the quantity inside the absolute value is positive and when it is negative.

Case 1: (2x - 4) ≥ 0
If 2x - 4 ≥ 0, we can remove the absolute value and rewrite the inequality as 3 - (2x - 4) ≤ 1. Simplifying this inequality gives us 7 - 2x ≤ 1. To solve for x, we subtract 7 from both sides and then divide by -2 (flipping the inequality direction due to dividing by a negative number):
-2x ≤ -6
x ≥ 3

Case 2: (2x - 4) < 0
If 2x - 4 < 0, the sign inside the absolute value changes when we remove the absolute value. So, we rewrite the inequality as 3 - (-(2x - 4)) ≤ 1. Simplifying further gives us 3 + 2x - 4 ≤ 1. Solving this inequality:
2x - 1 ≤ 1
2x ≤ 2
x ≤ 1

Combining the solutions from both cases, we find that the values of x that satisfy the inequality 3 - |2x - 4| ≤ 1 are:
x ≥ 3 and x ≤ 1