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