How do you solve `7( p + 1) + p = 9`?

`7(p+1)+p=9`
Distribute `\color(indianred)(7(p+1))\rArr\color(indianred)(7p+7(1))+p=9`
Add like terms `\rArr\color(mediumaquamarine)(8p)+7=9`
Subtract 7 from both sides `\rArr8p\cancel(+7)\cancel(\color(olive)(-7))=9\color(olive)(-7)`
`8p=2` divide both sides by 8 to isolate `p\rArr(\cancel(8)p)/\cancel(\color(seagreen)(8))=2/\color(seagreen)(8)`
`p=2/8`

plug in to check:
`7(2/8+1)+2/8\stackrel{?}{=}9`
`14/8+7+2/8\stackrel{?}{=}9`
`16/8+7\stackrel{?}{=}9`
`16/8\stackrel{?}{=}2`
`2=2`
the `p` value works!

To solve for `p`, we need to isolate it. This means we need to get everything else by itself.

`7(p+1)+p=9`

First, lets distribute the `7` across the parentheses.

`7p+7+p=9`

Now, let's combine like terms.

`8p+7=9`

Now get `8p` by itself.

`8p=2`

To get `p` by itself, we need to divide `8` from both sides.

`p = 2/8`

This is our answer, but it can still be simplified. Let's reduce the fraction.

`2/8 = 1/4`

So our final answer:

`p = 1/4`

To check the answer, just plug `1/4` back in to `p` in the original problem, and both sides should equal each other. They do in this case, so `1/4` is the correct solution.