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

2 Answers
Anirudh E.
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 #6p-(1-7p)#.

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--

#6p **-** (1-7p)#

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

#6p-(1-7p)#

#6p-1+7p#

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:

#6p-1+7p#

#6p+7p-1#

#13p-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. #13p-1# is the final answer!

I hope that helps!

Anthony R.
Aug 1, 2017

#13p-1#

Explanation:

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

#6pcolor(red)(-)(1-7p)->6pcolor(red)-1color(red)-(-7p)#

#6p-1+7p#

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

Thus,

#color(blue)(6p)-1color(blue)(+7p)#

#color(blue)(13p)-1larr# This is as much as we can do

We cannot combine #13p# 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(color(blue)3)-1#

#=39-1#

#=38#

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