First, subtract #color(red)(5)# from each side of the equation to isolate the absolute value term while keeping the equation balanced:
#3abs(2w - 2) + 5 - color(red)(5) = 29 - color(red)(5)#
#3abs(2w - 2) + 0 = 24#
#3abs(2w - 2) = 24#
Next, divide each side of the equation by #color(red)(3)# to isolate the absolute value function while keeping the equation balanced:
#(3abs(2w - 2))/color(red)(3) = 24/color(red)(3)#
#(color(red)(cancel(color(black)(3)))abs(2w - 2))/cancel(color(red)(3)) = 8#
#abs(2w - 2) = 8#
The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
Solution 1:
#2w - 2 = -8#
#2w - 2 + color(red)(2) = -8 + color(red)(2)#
#2w - 0 = -6#
#2w = -6#
#(2w)/color(red)(2) = -6/color(red)(2)#
#(color(red)(cancel(color(black)(2)))w)/cancel(color(red)(2)) = -3#
#w = -3#
Solution 2:
#2w - 2 = 8#
#2w - 2 + color(red)(2) = 8 + color(red)(2)#
#2w - 0 = 10#
#2w = 10#
#(2w)/color(red)(2) = 10/color(red)(2)#
#(color(red)(cancel(color(black)(2)))w)/cancel(color(red)(2)) = 5#
#w = 5#
The Solutions Are: #w = -3# and #w = 5#
