First, subtract #color(red)(12)# from each side of the equation to isolate the absolute value term while keeping the equation balanced:
#-color(red)(12) + 12 + 2abs(3x - 4) = -color(red)(12) + 8#
#0 + 2abs(3x - 4) = -4#
#2abs(3x - 4) = -4#
Next. divide each side of the equation by #color(red)(2)# to isolate the absolute value function while keeping the equation balanced:
#(2abs(3x - 4))/color(red)(2) = -4/color(red)(2)#
#(color(red)(cancel(color(black)(2)))abs(3x - 4))/cancel(color(red)(2)) = -2#
#abs(3x - 4) = -2#
The absolute value function takes any term and transforms it to its non-negative form.
Therefore, there is no value of #x# which will allow the absolute value function to equal a negative number. There are no solutions for this problem. Or, the solution is the null or empty set: #{O/}#
