Question

How do you solve and check your solutions to `-2/7v=16`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the equation by `color(red)(7)/color(blue)(-2)` to solve for `v` while keeping the equation balanced:

`color(red)(7)/color(blue)(-2) xx (-2)/7v = color(red)(7)/color(blue)(-2)xx 16`

`cancel(color(red)(7))/cancel(color(blue)(-2)) xx color(blue)(cancel(color(black)(-2)))/color(red)(cancel(color(black)(7)))v = color(red)(7)/(-cancel(color(blue)(2))) xx color(blue)(cancel(color(black)(16)))8`

`v = 56/-1`

`v = -56`

To check the solution, substitute `-56` for `v` in the original equation and ensure the left side of the equation calculates to `16`:

`-2/7v = 16` becomes:

`-2/7 * -56 = 16`

`-2/color(red)(cancel(color(black)(7))) * -8color(red)(cancel(color(black)(56))) = 16`

`-2 * -8 = 16`

`16 = 16`

The answer checks out.