were solving absolute value equations \can you help me out in 1

8-|3x-2|=3
i don't know if we distribute the negative or make it into -1 or its a no value something like that theirs no possible answer

subtract 8 from 3 then add two to that answerthen divide by 3. then u will get x

no that's not the answer since theirs always 2 answers to this and plus we cannot just do that since were suppose to eliminate everything else outside of the absolute valeu

arrange it like this:

8-3 = |3x-2|

so (3x-2) = 5 or -3x+2 = 5
3x = 7 or -3x = 3
x = 7/3 or x = -1

To solve the absolute value equation 8 - |3x - 2| = 3, we need to consider two cases:

Case 1: 3x - 2 is nonnegative (3x - 2 ≥ 0).
In this case, the absolute value |3x - 2| is simply equal to 3x - 2. So we can rewrite the equation as: 8 - (3x - 2) = 3.

Now let's solve for x:
8 - 3x + 2 = 3
-3x + 10 = 3
-3x = 3 - 10
-3x = -7
x = (-7) / (-3)
x = 7/3

Case 2: 3x - 2 is negative (3x - 2 < 0).
In this case, the absolute value |3x - 2| is the negative of its expression inside the absolute value symbol, so it becomes -(3x - 2). So we can rewrite the equation as: 8 - (-(3x - 2)) = 3.

Now let's solve for x:
8 + 3x - 2 = 3
3x + 6 = 3
3x = 3 - 6
3x = -3
x = -3 / 3
x = -1

Therefore, the solutions to the equation 8 - |3x - 2| = 3 are x = 7/3 and x = -1.