Question

How do you solve `-\frac { 3} { 2} y - \frac { 9} { 7} = - \frac { 3} { 2}`?

Answer 1

See the entire solution process below:

Explanation:

First, eliminate the fractions and keep the equation balanced by multiplying each side of the equation by `color(red)(14)`.

`color(red)(14)(-3/2y - 9/7) = color(red)(14) xx -3/2`

`(color(red)(14) xx -3/2y) - (color(red)(14) xx 9/7) = cancel(color(red)(14))7 xx -3/color(red)(cancel(color(black)(2)))`

`(cancel(color(red)(14))7 xx -3/color(red)(cancel(color(black)(2)))y) - (cancel(color(red)(14))2 xx 9/color(red)(cancel(color(black)(7)))) = -21`

`-21y - 18 = -21`

Next, add `color(red)(18)` to each side of the equation to isolate the `y` term while keeping the equation balanced:

`-21y - 18 + color(red)(18) = -21 + color(red)(18)`

`-21y - 0 = -3`

`-21y = -3`

Now, divide each side of the equation by `color(red)(-21)` to solve for `y` while keeping the equation balanced:

`(-21y)/color(red)(-21) = -3/color(red)(-21)`

`(color(red)(cancel(color(black)(-21)))y)/cancel(color(red)(-21)) = 1/7`

`y = 1/7`