First, multiply each side of the inequality by #color(red)(2)# to eliminate the fraction while keeping the inequality balanced:
#color(red)(2) xx (-x + 8)/2 >= color(red)(2) xx 3#
#cancel(color(red)(2)) xx (-x + 8)/color(red)(cancel(color(black)(2))) >= 6#
#-x + 8 >= 6#
Next, subtract #color(red)(8)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#-x + 8 - color(red)(8) >= 6 - color(red)(8)#
#-x + 0 >= -2#
#-x >= -2#
Now, multiply each side of the inequality by #color(blue)(-1)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#color(blue)(-1) xx -x color(red)(<=) color(blue)(-1) xx -2#
#x color(red)(<=) 2#
