How do you solve #abs(1/2x+4)=6#?

1 Answer
Mar 21, 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:

#1/2x + 4 = -6#

#1/2x + 4 - color(red)(4) = -6 - color(red)(4)#

#1/2x + 0 = -10#

#1/2x = -10#

#color(red)(2) xx 1/2x = color(red)(2) xx -10#

#color(red)(2)/2x = -20#

#1x = -20#

#x = -20#

Solution 2:

#1/2x + 4 = 6#

#1/2x + 4 - color(red)(4) = 6 - color(red)(4)#

#1/2x + 0 = 2#

#1/2x = 2#

#color(red)(2) xx 1/2x = color(red)(2) xx 2#

#color(red)(2)/2x = 4#

#1x = 4#

#x = 4#

The Solution Set Is: #x = {-20, 4}#