Question

How do you solve `-232= 6( - 7n + 3) - 8n`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in the parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Then group and combine common terms:

`-232 = color(red)(6)(-7n + 3) - 8n`

`-232 = (color(red)(6) xx -7n) + (color(red)(6) xx 3) - 8n`

`-232 = -42n + 18 - 8n`

`-232 = -42n - 8n + 18`

`-232 = (-42 - 8)n + 18`

`-232 = -50n + 18`

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

`-232 - color(red)(18) = -50n + 18 - color(red)(18)`

`-250 = -50n + 0`

`-250 = -50n`

Now, divide each side of the equation by `color(red)(-50)` to solve for `n` while keeping the equation balanced:

`(-250)/color(red)(-50) = (-50n)/color(red)(-50)`

`5 = (color(red)(cancel(color(black)(-50)))n)/cancel(color(red)(-50))`

`5 = n`

`n = 5`

Answer 2

`n = 5`

Explanation:

`−232=6 ("-"7n+3)−8n`      Solve for `n`

1) Clear the parentheses by distributing the `6`
After you have multiplied both of the terms inside the parentheses by 6, you will have this:
`- 232 = - 42 n + 18 - 8n`

2) Combine like terms
After you combine `-42 n` with `-8n`, you will get this
`-232 = -50 n + 18`

3) Subtract `18` from both sides to isolate the `-50  n` term
`-250 = - 50 n`

4) Divide both sides by `- 50` to isolate `n`
`5 = n`

Answer:
`n = 5`

`color(white)(mmmmmm)` ――――――――

Check

Sub in `5` in the place of `n` in the original equation

`−232=6 ("-"7 n  +3)−8 n`
`−232=6 ("-"7(5)+3)−8(5)`

1) Multiply   `"-"7(5)`  inside the parentheses
`−232=6 (-35+3)−8(5)`

2) Combine `-35` with `3` inside the parentheses
`−232=6  (-32)−8(5)`

3) Clear the parentheses by distributing the `6` and the `8`
`-232  = -192 - 40`

4) Combine like terms
`-232  = -232`

`Check`