First, subtract #color(red)(5)# from each side of the equation to isolate the absolute value term while keeping the equation balanced:

#5 - color(red)(5) + 8abs(-10n - 2) = 101 - color(red)(5)#

#0 + 8abs(-10n - 2) = 96#

#8abs(-10n - 2) = 96#

Next divide each side of the equation by #color(red)(8)# to isolate the absolute value function while keeping the equation balanced:

#(8abs(-10n - 2))/color(red)(8) = 96/color(red)(8)#

#(color(red)(cancel(color(black)(8)))abs(-10n - 2))/cancel(color(red)(8)) = 12#

#abs(-10n - 2) = 12#

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:**

#-10n - 2 = -12#

#-10n - 2 + color(red)(2) = -12 + color(red)(2)#

#-10n - 0 = -10#

#-10n = -10#

#(-10n)/color(red)(-10) = (-10)/color(red)(-10)#

#(color(red)(cancel(color(black)(-10)))n)/cancel(color(red)(-10)) = 1#

#n = 1#

**Solution 2:**

#-10n - 2 = 12#

#-10n - 2 + color(red)(2) = 12 + color(red)(2)#

#-10n - 0 = 14#

#-10n = 14#

#(-10n)/color(red)(-10) = 14/color(red)(-10)#

#(color(red)(cancel(color(black)(-10)))n)/cancel(color(red)(-10)) = -14/10#

#n = -14/10#

**The Solutions Are:** #n = 1# **and** #n = -14/10#