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}
