Because both sides of the equation are pure fractions we can flip the fractions giving:

#100/2400 = x/180#

Next, we can reduce the fraction on the left side of the equation:

#1/24 = x/180#

Now, we can multiply each side of the equation by #color(red)(180)# to solve for #x# while keeping the equation balanced:

#color(red)(180) xx 1/24 = color(red)(180) xx x/180#

#color(red)((12 xx 15)) xx 1/((12 xx 2)) = cancel(color(red)(180)) xx x/color(red)(cancel(color(black)(180)))#

#color(red)((color(black)(cancel(color(black)(12))) xx 15)) xx 1/((color(red)(cancel(color(black)(12))) xx 2)) = x#

#15/2 = x#

#x = 15/2#

Another process would be to first reduce the fraction on the left side of the equation:

#24/1 = 180/x#

#24 = 180/x#

Now, multiply each side of the equation by #color(red)(x)/color(blue)(24)# to solve for #x# while keeping the equation balanced:

#color(red)(x)/color(blue)(24) xx 24 = color(red)(x)/color(blue)(24) xx 180/x#

#color(red)(x)/cancel(color(blue)(24)) xx color(blue)(cancel(color(black)(24))) = cancel(color(red)(x))/(color(blue)(12 xx 2)) xx (12 xx 15)/color(red)(cancel(color(black)(x)))#

#x = 1/(color(blue)(color(black)(cancel(color(blue)(12))) xx 2)) xx (color(blue)(cancel(color(black)(12))) xx 15)/1#

#x = 15/2#