First, subtract #color(red)(5)# from each side of the equation to isolate the absolute value term and keep the equation balanced:
#5 - 2abs(3x - 4) - color(red)(5) = -5 - color(red)(5)#
#5 - color(red)(5) - 2abs(3x - 4) = -10#
#0 - 2abs(3x - 4) = -10#
#-2abs(3x - 4) = -10#
Next, divide each side of the equation by #color(red)(-2)# to solve for the absolute value term while keeping the equation balanced:
#(-2abs(3x - 4))/color(red)(-2) = (-10)/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))abs(3x - 4))/cancel(color(red)(-2)) = 5#
#abs(3x - 4) = 5#
The absolute value is a special function requiring two solutions. The function transforms a negative or positive term to its positive form. Therefore the term inside the absolute value must be solve for the both the negative and positive term it is equate to.
Solution 1)
#3x - 4 = -5#
#3x - 4 + 4 = -5 + 4#
#3x - 0 = -1#
#3x = -1#
#(3x)/3 = -1/3#
#(color(red)(cancel(color(black)(3)))x)/color(red)(cancel(color(black)(3))) = -1/3#
#x = -1/3#
Solution 2)
#3x - 4 = 5#
#3x - 4 + 4 = 5 + 4#
#3x - 0 = 9#
#3x = 9#
#(3x)/3 = 9/3#
#(color(red)(cancel(color(black)(3)))x)/color(red)(cancel(color(black)(3))) = 3#
#x = 3#
The solution to this problem is:
#x = -1/3# and #x = 3#
