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#
