Question

How do you solve `-\frac { 2} { 3} y + 8= 26`?

Answer 1

`y=-27`

Explanation:

Solve:

`-2/3y+8=26`

Rewrite `-2/3y` as `-(2y)/3`

`-(2y)/3+8=26`

Subtract `8` from both sides.

`-(2y)/3+color(red)cancel(color(black)(8))-color(red)cancel(color(black)(8))=26-8`

Simplify.

`-(2y)/3=18`

Multiply both sides by `3`.

`-(2y)/color(red)cancel(color(black)(3))xxcolor(red)cancel(color(black)(3))=18xx3`

Simplify.

`-2y=54`

Divide both sides by `-2`.

`(color(red)cancel(color(black)(-2))y)/(color(red)cancel(color(black)(-2)))=54/(-2)`

Simplify. (A negative divided by a negative makes a positive, and a positive divided by a negative makes a negative.)

`y=-27`

Check.

`-2/3xxcolor(green)(-27)+8=26`

Answer 2

See the entire solution process below:

Explanation:

First, subtract `color(red)(8)` from each side of the equation to isolate the `y` term while keeping the equation balanced:

`-2/3y + 8 - color(red)(8) = 26 - color(red)(8)`

`-2/3y + 0 = 18`

`-2/3y = 18`

Now, multiply each side of the equation by `color(red)(3)/color(blue)(-2)` to solve for `y` while keeping the equation balanced:

`color(red)(3)/color(blue)(-2) * (-2)/3y = color(red)(3)/color(blue)(-2) * 18`

`cancel(color(red)(3))/cancel(color(blue)(-2)) * color(blue)(cancel(color(black)(-2)))/color(red)(cancel(color(black)(3)))y = 54/color(blue)(-2)`

`y = -27`