Question

How do you solve: `n + 2 = -14 - n`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(2)` and add `color(blue)(n)` to each side of the equation to isolate the `n` term while keeping the equation balanced:

`n + 2 - color(red)(2) + color(blue)(n) = -14 - n - color(red)(2) + color(blue)(n)`

`n + color(blue)(n) + 2 - color(red)(2) = -14 - color(red)(2) - n + color(blue)(n)`

`1n + 1color(blue)(n) + 0 = -16 - 0`

`2n = -16`

Now, divide each side of the equation by `color(red)(2)` to solve for `n` while keeping the equation balanced:

`(2n)/color(red)(2) = -16/color(red)(2)`

`(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) = -8`

`n = -8`

Answer 2

`n=-8`

Explanation:

To solve this equation, collect terms in n on the left side and numeric values on the right side.

add n to both sides.

`n+n+2=-14cancel(-n)cancel(+n)`

`rArr2n+2=-14`

subtract 2 from both sides.

`2ncancel(+2)cancel(-2)=-14-2`

`rArr2n=-16`

divide both sides by 2

`(cancel(2) n)/cancel(2)=(-16)/2`

`rArrn=-8`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side equals the right side then it is the solution.

`"left side " =-8+2=-6`

`"right side " =-14-(-8)=-14+8=-6`

`rArrn=-8" is the solution"`

Answer 3

`n =-8`

Explanation:

You need to get all the variables (`n`) on one side and all the numbers on the other.
You want to get to the answer: `n = "a value"`

In an equation, you have to do the SAME to BOTH sides, otherwise the sides will no longer be equal.

`n+2 =-14-n" "larr` add `n` to each side first

`n+2color(red)(+n) =-14-n color(red)(+n)`

`2n +2 = -14" "larr` subtract `2` from from sides

`2n +2 color(blue)(-2)= -14 color(blue)(-2)`

`2n = -16" "larr div 2` to isolate `n`

`(2n)/2 = (-16)/2`

`n =-8`

Note that `-n color(red)(+n) =0" " and " " +2 color(blue)(-2)=0`

Answer 4

`n="-"8`

Explanation:

First add `n` to both sides to eliminate it from the right side
`n+2color(green)(+n)="-"14color(red)(cancelcolor(black)(-n)cancelcolor(green)(+n))`
`2n+2="-"14`

Then subtract `2` from both sides to isolate the `n` term on the left side
`2ncolor(red)(cancelcolor(black)(+2)cancelcolor(green)(-2))="-"14color(green)(-2)`
`2n="-"16`

Finally divide both sides by `2` to isolate `n`
`color(green)((color(red)cancelcolor(black)2color(black)n)/color(red)cancelcolor(green)2)=color(green)(color(black)("-"16)/2)`
`n="-"8`