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.
#-3 >= 5 - x >= 3#
First, subtract #color(red)(5)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:
#-color(red)(5) - 3 >= -color(red)(5) + 5 - x >= -color(red)(5) + 3#
#-8 >= 0 - x >= -2#
#-8 >= -x >= -2#
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) xx -8 color(red)(<=) color(blue)(-1) xx -x color(red)(<=) color(blue)(-1) xx -2#
#8 color(red)(<=) x color(red)(<=) 2#
Or
#x <= 2#; #x >= 8#
Or, in interval notation:
#(-oo, 2]#; #[8, +oo)#
