How do you solve #abs(7x+1/8 )=2#?

1 Answer
Mar 20, 2018

Answer:

See a solution process below:

Explanation:

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}#