The absolute value function takes any negative or positive 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.
#-13 >= 8 - x >= 13#
First, subtract #color(red)(8)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:
#-color(red)(8) - 13 >= -color(red)(8) + 8 - x >= -color(red)(8) + 13#
#-21 >= 0 - x >= 5#
#-21 >= -x >= 5#
Now, multiply each segment by #color(blue)(-1)# to solve for #x# while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we must reverse the inequality operators:
#color(blue)(-1) * -21 color(red)(<=) color(blue)(-1) * -x color(red)(<=) color(blue)(-1) * 5#
#21 color(red)(<=) x color(red)(<=) -5#
Or
#x <= -5#; #x >= 21#
Or, in interval notation:
#(-oo, -5]#; #[21, +oo)#
