Since there is a multiplier of 7 on the left, and both terms on the right are divisible by 7, I'd start by dividing the equation by 7
|8 - 3x| = 3x - 7
The absolute value function may or may not negate its argument. (The argument is negated if it is negative.) Hence this can resolve to two equations
-(8 -3x) = 3x -7
or
(8 -3x) = 3x -7
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Starting with the first of these, we can eliminate parentheses to get
... -8 +3x = 3x -7
Subtracting 3x from both sides gives the FALSE statement
... -8 = -7 . . . . FALSE
Thus, this version of the equation has No Solution.
Looking at the second of the equations above, we can add 3x to get
... 8 = 6x -7
Adding 7 and dividing by 6 gives
... (8 +7)/6 = x = 5/2
The solution is x = 5/2.
