# How do you combine 6p - ( 1- 7p )?

Aug 1, 2017

Use the distributive property to distribute the negative sign. See explanation below.

#### Explanation:

In mathematics, there is a fundamental property that you should be aware of. This is known as the distributive property.

In the case of this question, we are asked to combine $6 p - \left(1 - 7 p\right)$.

Since we are asked to subtract two terms at once, this may seem a little difficult at first. But thanks to our friend the Distribute Property, we can distribute the negative sign in front of the parentheses--

$6 p \ast - \ast \left(1 - 7 p\right)$

--to the terms within the parentheses. If that sounded a little confusing, we just have to multiply $1 - 7 p$ by $- 1$ as our first step:

$6 p - \left(1 - 7 p\right)$

$6 p - 1 + 7 p$

As you can see, all we had to do really was flip the signs of the two terms within the parentheses.

Next, we have to combine like terms. If you take a look at what we have so far, there are $2$ terms with $p$ and some coefficient in the front. So let's combine those $2$ terms:

$6 p - 1 + 7 p$

$6 p + 7 p - 1$

$13 p - 1$

Now, let's check to see if we are done. Since all of the like terms have been combined and no other operations can be completed without further information, we are finished. $13 p - 1$ is the final answer!

I hope that helps!

Aug 1, 2017

$13 p - 1$

#### Explanation:

Well we can start by distributing the negative to both $1$ and $- 7 p$.

$6 p \textcolor{red}{-} \left(1 - 7 p\right) \to 6 p \textcolor{red}{-} 1 \textcolor{red}{-} \left(- 7 p\right)$

$6 p - 1 + 7 p$

Now we can combine like terms. Here, both $6 p$ and $7 p$ are like terms because they both have a variable $p$.

Thus,

$\textcolor{b l u e}{6 p} - 1 \textcolor{b l u e}{+ 7 p}$

$\textcolor{b l u e}{13 p} - 1 \leftarrow$ This is as much as we can do

We cannot combine $13 p$ and $- 1$ since they are not like terms. If we knew the value for $p$ then we could combine them. For example, say $p = 3$, then...

$13 \left(\textcolor{b l u e}{3}\right) - 1$

$= 39 - 1$

$= 38$