Question

How do you solve `-6n-10=-2n+4(1-3n)`?

Answer 1

`n=1.75`

Explanation:

This might look a little intimidating, but the process is fairly straightforward.
To begin, let's distribute the `4`, so that the problem becomes `-6n-10=-2n+4-12n`.
From here, we should combine like-terms. That leaves us with
`-6n-10=-14n+4`.

We need to isolate the variable, so our next step should be to move all the constants to one side and all the variables to the other.

`-6n-10=-14n+4`
`color(green)(+14n)color(white)()color(purple)(+10)=color(green)(+14n)color(white)(.)color(purple)(+10)`

Now we have `8n=14`, and if we divide by `8` on both sides we have `n=14/8` or `1.75`.

Answer 2

`n=7/4`

Explanation:

The first step is to distribute the bracket.

`rArr-6n-10=-2n+4-12n`

`rArr-6n-10=-14n+4`

Collect terms in n on the left side and numeric values on the right side.

add 14n to both sides.

`-6n+14n-10=cancel(-14n)cancel(+14n)+4`

`rArr8n-10=4`

add 10 to both sides.

`8ncancel(-10)cancel(+10)=4+10`

`rArr8n=14`

divide both sides by 8

`(cancel(8) n)/cancel(8)=14/8`

`rArrn=14/8=7/4`

`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 "=(-6xx7/4)-10=-21/2-10=-41/2`

`"right side "=(-2xx7/4)+4(1-3xx7/4)`

`color(white)(right sidexx)=-7/2+4(1-21/4)`

`color(white)(right sidexx)=-7/2-17=-41/2`

`rArrn=7/4" is the solution"`