How do you solve \frac { 11m + 6} { 7} = \frac { m } { 9}?

2 Answers
Aug 7, 2017

See a solution process below:

Explanation:

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

Aug 7, 2017

m = -27/46

Explanation:

9(11m+6)=7m

99m+54=7m

99m-7m=-54

92m= -54

m=-54/92