First subtract #color(red)(2x)# and add #color(blue)(7)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#-color(red)(2x) + 2x + 15 + color(blue)(7) >= -color(red)(2x) + 4x - 7 + color(blue)(7)#
#0 + 22 >= (-color(red)(2) + 4)x - 0#
#22 >= 2x#
Now, divide each side of the equation by #color(red)(2)# to solve for #x# while keeping the equation balanced:
#22/color(red)(2) >= (2x)/color(red)(2)#
#11 >= (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))#
#11 >= x#
To state the solution in terms of #x# we can reverse or "flip" the entire inequality:
#x <= 11#
