First, subtract #color(blue)(55)# from each side of the inequality to isolate the #z# term while keeping the inequality balanced:
#108 - color(blue)(55) > z/-2 + 55 - color(blue)(55)#
#53 > z/-2 + 0#
#53 > z/-2#
Now, multiply each side of the inequality by #color(blue)(-2)# to solve for #z# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we need to reverse the inequality operator:
#color(blue)(-2) xx 53 color(red)(<) color(blue)(-2) xx z/-2#
#-106 color(red)(<) cancel(color(blue)(-2)) xx z/color(blue)(cancel(color(black)(-2)))#
#-106 < z#
To state in terms of #z# we need to reverse or "flip" the entire inequality:
#z > -106#
