First, subtract #color(red)(5)# from each side of the equation to isolate the absolute value term while keeping the equation balanced:
#3abs(9x) + 5 - color(red)(5) = 26 - color(red)(5)#
#3abs(9x) + 0 = 21#
#3abs(9x) = 21#
Next, divide each side of the equation by #color(red)(3)# to isolate the absolute value term while keeping the equation balanced:
#(3abs(9x))/color(red)(3) = 21/color(red)(3)#
#(color(red)(cancel(color(black)(3)))abs(9x))/cancel(color(red)(3)) = 7#
#abs(9x) = 7#
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:
#9x = -7#
#(9x)/color(red)(9) = -7/color(red)(9)#
#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = -7/9#
#x = -7/9#
Solution 2:
#9x = 7#
#(9x)/color(red)(9) = 7/color(red)(9)#
#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 7/9#
#x = 7/9#
The Solution Is:
#x = {-7/9, 7/9}#
