Question

How do you solve `3n + 15= 4-4n - 3`?

Answer 1

Collect 'like terms': all the terms containing 'n' on the left, all the numbers not containing 'n' on the right. If we move anything to the opposite side of the equals sign we change its sign:

`n= -8/7`

Explanation:

`3n+15=4-4n-3`

Collect the like terms on the right:

`3n+15=-4n+4-3`
`=-4n+7`

Subtract `15` from both sides:

`3n=-4n+7-15`
`=-4n-8`

Add `4n` to both sides:

`3n+4n=-8`

`7n=-8`

Divide both sides by `7`:

`n= -8/7`

Answer 2

See a solution process below:

Explanation:

First, group and combine like terms on the right side of the equation:

`3n + 15 = 4 - 4n - 3`

`3n + 15 = -4n + 4 - 3`

`3n + 15 = -4n + 1`

Next, subtract `color(red)(15)` and add `color(blue)(4n)` to each side of the equation to isolate the `n` term while keeping the equation balanced:

`color(blue)(4n) + 3n + 15 - color(red)(15) = color(blue)(4n) - 4n + 1 - color(red)(15)`

`(color(blue)(4) + 3)n + 0 = 0 - 14`

`7n = -14`

Now, divide each side of the equation by `color(red)(7)` to solve for `n` while keeping the equation balanced:

`(7n)/color(red)(7) = -14/color(red)(7)`

`(color(red)(cancel(color(black)(7)))n)/cancel(color(red)(7)) = -2`

`n = -2`