First, multiply each side of the equation by #color(red)(2)# to eliminate the fraction while keeping the equation balanced:
#color(red)(2)(5 + 1/2x) = color(red)(2)(5x - 22)#
#(color(red)(2) xx 5) + (color(red)(2) xx 1/2x) = (color(red)(2) xx 5x) - (color(red)(2) xx 22)#
#10 + (cancel(color(red)(2)) xx 1/color(red)(cancel(color(black)(2)))x) = 10x - 44#
#10 + 1x = 10x - 44#
Next, subtract #color(red)(1x)# and add #color(blue)(44)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#10 + 1x - color(red)(1x) + color(blue)(44) = 10x - 44 - color(red)(1x) + color(blue)(44)#
#10 + color(blue)(44) + 1x - color(red)(1x) = 10x - color(red)(1x) - 44 + color(blue)(44)#
#54 + 0 = (10 - color(red)(1))x - 0#
#54 = 9x#
Now, divide each side of the equation by #color(red)(9)# to solve for #x# while keeping the equation balanced:
#54/color(red)(9) = (9x)/color(red)(9)#
#6 = (color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9))#
#6 = x#
#x = 6#
