Question

How do you solve `4v - 9( v - 9) = 46`?

Answer 1

See the entire solution process below:

Explanation:

First, eliminate the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`4v - color(red)(9)(v - 9) = 46`

`4v - (color(red)(9) xx v) + (color(red)(9) xx 9) = 46`

`4v - 9v + 81 = 46`

Next, combine the like terms on the left side of the equation:

`(4 - 9)v + 81 = 46`

`-5v + 81 = 46`

Then, subtract `color(red)(81)` from each side of the equation to isolate the `v` term while keeping the equation balanced:

`-5v + 81 - color(red)(81) = 46 - color(red)(81)`

`-5v + 0 = -35`

`-5v = -35`

Now, divide each side of the equation by `color(red)(-5)` to solve for `v` while keeping the equation balanced:

`(-5v)/color(red)(-5) = (-35)/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))v)/cancel(color(red)(-5)) = 7`

`v = 7`