anonymous
  • anonymous
Two thirds of a number added to 6 is equal to the number. What is this number?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Let's start by: Let x = the unknown number
anonymous
  • anonymous
0k
anonymous
  • anonymous
Here's what we're looking at: 2/3 of a number added to 6 is the number

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anonymous
  • anonymous
Let's translate that directly into math.
anonymous
  • anonymous
Do you remember what the word "of" means?
anonymous
  • anonymous
Divide
anonymous
  • anonymous
Not divide... the other one. :)
anonymous
  • anonymous
(on a side note, usually the word 'per' means divide)
anonymous
  • anonymous
multiply?
anonymous
  • anonymous
That's right - multiply! :)
anonymous
  • anonymous
2/3 of a number added to 6 is the number So we can change the line above to: (2/3) (a number) added to 6 is the number
anonymous
  • anonymous
Now, what did we decide we were going to call our unknown number?
anonymous
  • anonymous
x
anonymous
  • anonymous
That's right. Now, do you remember what the word "is" means?
anonymous
  • anonymous
"is" is the conjugation of the English verb "to be" for he/she/it or a noun/proper noun.
anonymous
  • anonymous
So far, we have: (2/3) (x) added to 6 is (x)
anonymous
  • anonymous
Yes, but what does it mean in the language of mathematics?
anonymous
  • anonymous
I forgot :(
anonymous
  • anonymous
What it's equal to?
anonymous
  • anonymous
Exactly! Is means "="
anonymous
  • anonymous
So far, we have: (2/3) (x) added to 6 = (x)
anonymous
  • anonymous
yes
anonymous
  • anonymous
Now, there's a little trick with the language here. If we have 2/3x added to 6, it would be translated like this: 6 + (2/3)(x) = (x) Remember, if it is "added to" 6 that means we have the 6 first, and we added the 2/3x to it.
anonymous
  • anonymous
Does that make sense?
anonymous
  • anonymous
I believe so, yes.
anonymous
  • anonymous
So, our equation is: 6 + 2/3 x = x
anonymous
  • anonymous
mm hmm
anonymous
  • anonymous
So, what would we do to solve this? \[6 + \frac{2}{3} x = x\]
anonymous
  • anonymous
uhm
anonymous
  • anonymous
Take away six and have 2/x = x + 6
anonymous
  • anonymous
Well, if we take away six, we would have: \[\frac{2}{3} x = x-6\]
anonymous
  • anonymous
Although - instead of that... \[6 + \frac{2}{3} x = x\]Recognize that we have a fraction here.
anonymous
  • anonymous
Let's clear the fraction by multiplying each piece by 3.
anonymous
  • anonymous
\[(3)6 + (3)\frac{2}{3} x =(3) x\]
anonymous
  • anonymous
From there: \[18 + 2x = 3x\]
anonymous
  • anonymous
18 + 2 + 3z
anonymous
  • anonymous
Well, the variable would still be with the 2.
anonymous
  • anonymous
18+2z=3z
anonymous
  • anonymous
Yes, now what?
anonymous
  • anonymous
Cover one of 'em up! And you realize that x equals 6! :D
anonymous
  • anonymous
Not quite...
anonymous
  • anonymous
18+2z=3z -2z -2z 18=z
anonymous
  • anonymous
Oh thanks
anonymous
  • anonymous
do you believe in god?
anonymous
  • anonymous
So the number we're looking for is 18. :) You're welcome!!
anonymous
  • anonymous
Do you believe in God?
anonymous
  • anonymous
Does my medal depend on my answer to that question?
anonymous
  • anonymous
yup
anonymous
  • anonymous
My answer is 'no'

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