where does the 11 come from? (fraction)

x + 8/3x = 77

I don't understand how it becomes

11x/3 = 77

can someone help me please?

\(\displaystyle \displaystyle{x + \frac{8}{3} * x}\)

Factor out x

\(\displaystyle \displaystyle{= \ x * \left [ 1 + \frac{8}{3}\right ]}\)

\(\displaystyle \displaystyle{= \ x * \left [ \frac{11}{3}\right ]}\)

and you are done....
 
\(\displaystyle \displaystyle{x + \frac{8}{3} * x}\)

Factor out x

\(\displaystyle \displaystyle{= \ x * \left [ 1 + \frac{8}{3}\right ]}\)

\(\displaystyle \displaystyle{= \ x * \left [ \frac{11}{3}\right ]}\)

and you are done....

what did you do to get the 11? 8 plus 3?
 
I get the sense that the actual calculations involved are not what's causing the difficulties, but instead it's the mere fact that it's... dun dun dun... algebra. I say that in good fun, of course, because you're far from the first student I've encountered whose brain seems to go on strike when they encounter letters in their math. To perhaps make things easier, let's consider the essence of what the problem's asking. Begin with the statement, leaving off the equals portion for a moment:

x + (8/3)x

Now, here we have 1 whole something and we're given 8/3 of another something. We can think of 1 as 3/3. So, that leaves us with:

3/3 + 8/3

Now, these are perfectly ordinary fractions, nothing special about them whatsoever, so we add straight across, same as always. That leaves us with 11/3. Now, remember that we don't just have 11/3, we have 11/3 of something. But what's that something? Well, we don't know, but we're using the letter x as a placeholder. Return to the original equation and we now have:

(11/3)x = 77

Now, what do you think your next step would be?
 
Now, these are perfectly ordinary fractions, nothing special about them whatsoever, so we add straight across, same as always. That leaves us with 11/3. Now, remember that we don't just have 11/3, we have 11/3 of something. But what's that something? Well, we don't know, but we're using the letter x as a placeholder. Return to the original equation and we now have:

(11/3)x = 77

Now, what do you think your next step would be?

I think we have to isolate x now right? so I can multiple both sides by 3 to get rid of fraction so it becomes 11x = 231

then get rid of 11 to leave x alone so it goes x=231/11 and x = 21

thanks a lot, I really appreciate it. We moved to north America when I was about 11 or 12 years old and this was around the time they were teaching this in school, but since I didn't understand English at all I fell behind and never really caught up on it.
 
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