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:
#7x + 1/8 = -2#
#7x + 1/8 - color(red)(1/8) = -2 - color(red)(1/8)#
#7x + 0 = (8/8 xx -2) - color(red)(1/8)#
#7x = -16/8 - color(red)(1/8)#
#7x = -17/8#
#color(red)(1/7) xx 7x = color(red)(1/7) xx -17/8#
#7/color(red)(7)x = -17/56#
#1x = -17/56#
#x = -17/56#
Solution 2:
#7x + 1/8 = 2#
#7x + 1/8 - color(red)(1/8) = 2 - color(red)(1/8)#
#7x + 0 = (8/8 xx 2) - color(red)(1/8)#
#7x = 16/8 - color(red)(1/8)#
#7x = 15/8#
#color(red)(1/7) xx 7x = color(red)(1/7) xx 15/8#
#7/color(red)(7)x = 15/56#
#1x = 15/56#
#x = 15/56#
The Solution Set Is: #x = {-17/56, 15/56}#
