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.
#-8 <= 4 - 2x <= 8#
First, subtract #color(red)(4)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:
#-8 - color(red)(4) <= 4 - color(red)(4) - 2x <= 8 - color(red)(4)#
#-12 <= 0 - 2x <= 4#
#-12 <= -2x <= 4#
Now, divide each segment by #color(blue)(-2)# to solve for #x# while keeping the system balanced. However, because we are dividing inequalities by a negative number we must reverse the inequality operators:
#(-12)/color(blue)(-2) color(red)(>=) (-2x)/color(blue)(-2) color(red)(>=) 4/color(blue)(-2)#
#6 color(red)(>=) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(>=) -2#
#6 >= x >= -2#
Or
#x >= -2#; #x <= 6#
Or, in interval notation
#[-2, 6]#
