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.