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

Nov 19, 2016

$p = \frac{2}{8}$

Explanation:

$7 \left(p + 1\right) + p = 9$
Distribute $\setminus \textcolor{\in \mathrm{di} a n red}{7 \left(p + 1\right)} \setminus \Rightarrow \setminus \textcolor{\in \mathrm{di} a n red}{7 p + 7 \left(1\right)} + p = 9$
Add like terms $\setminus \Rightarrow \setminus \textcolor{m e \mathrm{di} u m a q u a m a r \in e}{8 p} + 7 = 9$
Subtract 7 from both sides $\setminus \Rightarrow 8 p \setminus \cancel{+ 7} \setminus \cancel{\setminus \textcolor{o l i v e}{- 7}} = 9 \setminus \textcolor{o l i v e}{- 7}$
$8 p = 2$ divide both sides by 8 to isolate $p \setminus \Rightarrow \frac{\setminus \cancel{8} p}{\setminus} \cancel{\setminus \textcolor{s e a g r e e n}{8}} = \frac{2}{\setminus} \textcolor{s e a g r e e n}{8}$
$p = \frac{2}{8}$

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!

Nov 19, 2016

$p = \frac{1}{4}$

Explanation:

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

$7 \left(p + 1\right) + p = 9$

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

$7 p + 7 + p = 9$

Now, let's combine like terms.

$8 p + 7 = 9$

Now get $8 p$ by itself.

$8 p = 2$

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

$p = \frac{2}{8}$

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

$\frac{2}{8} = \frac{1}{4}$

$p = \frac{1}{4}$
To check the answer, just plug $\frac{1}{4}$ back in to $p$ in the original problem, and both sides should equal each other. They do in this case, so $\frac{1}{4}$ is the correct solution.