Question

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

Answer 1

`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`