How do you solve \frac { 9} { 4} ( \frac { 41} { 6} b + \frac { 4} { 3} ) - \frac { 15} { 4} = - \frac { 2859} { 40}?

1 Answer
Sep 2, 2017

b= -23/5

Explanation:

First put the -15/4 to the other side to make it positive and add it

to the -2859/40. -15/4 must have a denominator of 40 so

multiply by 10 to get -150/40.

9/4(41/6 b +4/3) = -2859/40 + 150/40

9/4(41/6 b +4/3) = -2709/40

Now divide by 9/4 to get rid of the multiplication but you also have to divide -2709/40 by 9/4 as well.

(9/4(41/6 b +4/3))/(9/4) = (-2709/40)/(9/4)

The two 9/4 cancel out. Now the problem looks like this:

41/6 b +4/3= -10836/360

Now subtract 4/3:

41/6 b = -10836/360 - 4/3 -> 41/6 b = -943/30

Multiply by 6 to get rid of the denominator:

41b = -943/30 *6 -> 41b = -943/5

Finally, divide by 41 to isolate b.

b = (-943/5)/41

b = -23/5