First, multiply each side of the equation by #color(red)(63)# to eliminate the fractions while keeping the equation balanced. #color(red)(63)# is the lowest common denominator of the two fractions:
#color(red)(63) xx (11m + 6)/7 = color(red)(63) xx m/9#
#cancel(color(red)(63))9 xx (11m + 6)/color(red)(cancel(color(black)(7))) = cancel(color(red)(63))7 xx m/color(red)(cancel(color(black)(9)))#
#(9 xx 11m) + (9 xx 6) = 7m#
#99m + 54 = 7m#
Next, subtract #color(red)(54)# and #color(blue)(7m)# from each side of the equation to isolate the #m# term while keeping the equation balanced:
#-color(blue)(7m) + 99m + 54 - color(red)(54) = -color(blue)(7m) + 7m - color(red)(54)#
#(-color(blue)(7) + 99)m + 0 = 0 - 54#
#92m = -54#
Now, divide each side of the equation by #color(red)(92)# to solve for #m# while keeping the equation balanced:
#(92m)/color(red)(92) = -54/color(red)(92)#
#(color(red)(cancel(color(black)(92)))m)/cancel(color(red)(92)) = (2 xx -27)/color(red)(2 xx 46)#
#m = (color(red)(cancel(color(black)(2))) xx -27)/color(red)(color(black)(cancel(color(red)(2))) xx 46)#
#m = -27/46#
