Question

How do you solve `9= \frac { - 6} { 7} ( - 9- 9B)`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(7)/color(blue)(-6)` to eliminate the need for the parenthesis while keeping the equation balanced:

#color(red)(7)/color(blue)(-6) xx 9 = color(red)(7)/color(blue)(-6) xx (-6)/7(-9 - 9B)#

`-63/6 = (-42)/-42(-9 - 9B)`

`-63/6 = 1(-9 - 9B)`

`-63/6 = -9 - 9B`

Next, add `color(red)(9)` to each side of the equation to isolate the `B` term while keeping the equation balanced:

`color(red)(9) - 63/6 = color(red)(9) - 9 - 9B`

`(6/6 xx color(red)(9)) - 63/6 = 0 - 9B`

`54/6 - 63/6 = 0 - 9B`

`(54 - 63)/6 = 0 - 9B`

`(-9)/6 = -9B`

Now, divide each side of the equation by `color(red)(-9)` to solve for `B` while keeping the equation balanced:

`((-9)/6)/color(red)(-9) = (-9B)/color(red)(-9)`

`(-9)/(6 xx color(red)(-9)) = (color(red)(cancel(color(black)(-9)))B)/cancel(color(red)(-9))`

`color(red)(cancel(color(black)(-9)))/(6 xx cancel(color(red)(-9))) = B`

`1/6 = B`

`B = 1/6`