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
