How do you solve #abs(4n + 7) = 1#?

1 Answer
Mar 11, 2018

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:

#4n + 7 = -1#

#4n + 7 - color(red)(7) = -1 - color(red)(7)#

#4n + 0 = -8#

#4n = -8#

#(4n)/color(red)(4) = -8/color(red)(4)#

#(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) = -2#

#n = -2#

Solution 1:

#4n + 7 = 1#

#4n + 7 - color(red)(7) = 1 - color(red)(7)#

#4n + 0 = -6#

#4n = -6#

#(4n)/color(red)(4) = -6/color(red)(4)#

#(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) = -3/2#

#n = -3/2#

The Solution Set Is:

#n = {-2, -3/2}#