Rearranging Formula, making x the subject from y=5(x+3)

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Discussion Overview

The discussion revolves around rearranging the equation $$y=5(x+3)$$ to make $$x$$ the subject. Participants explore different approaches to isolating $$x$$ and express confusion regarding a discrepancy between their solution and that of their lecturer.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant presents their working as $$\frac{y}{5}-3=x$$, claiming it is correct and consistent with other sources like Mathway.
  • Another participant asks for the complete problem statement to clarify the context of the question.
  • Some participants confirm the correctness of the initial working and suggest substituting $$y=1.2$$ to find the corresponding $$x$$ value.
  • There is a discussion about the nature of the equation, with one participant noting that $$\frac{y}{5}-3=x$$ is a relation that can yield different $$x$$ values for different $$y$$ inputs.
  • One participant expresses confusion about how the lecturer arrived at $$x=1.2$$ from the equation, despite understanding that both their and the lecturer's examples are valid.
  • Another participant clarifies that the lecturer likely chose $$x=1.2$$ arbitrarily, emphasizing that the method of finding $$x$$ is what is being assessed.
  • One participant acknowledges their misunderstanding and recognizes that $$x$$ can take on any value, highlighting the focus on the method rather than the specific value of $$x$$.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the rearrangement process, but there is confusion regarding the specific value of $$x$$ chosen by the lecturer. Multiple views on the interpretation of the problem and the nature of the solutions remain present.

Contextual Notes

Participants express uncertainty about the lecturer's reasoning and the arbitrary nature of the chosen values for $$x$$. The discussion highlights the importance of understanding the method of rearranging equations rather than focusing solely on specific numerical examples.

Subliminal1
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Hi, we were rearranging formula to make $$x$$ the subject and for one equation our answer was different to our lecturers, but they failed to explain why they were right and we were wrong- if someone could that would be great.

The equation with our working:

$$y=5\left(x+3\right)$$

$$\frac{y}{5}=x+3$$

$$\frac{y}{5}-3=x$$

We're told to do "the opposite" for this, so:
We isolated the variable ($$x$$) by dividing each side by factors that don't contain the variable ($$5$$).
Then it's simple by subtracting $$3$$ from $$x$$.
Replacing $$x$$ with 2 as an example to test our result:

$$y=5\left(2+3\right)$$ (or) $$y=5$$x$$5$$ (or) $$y=25$$

$$\frac{25}{5}=5$$, $$−3=2$$, $$x=2$$

Even Mathway gives the same working, so I'm a little lost. I can't remember exactly what our lecturer said the answer was, I believe it was $$y=1.2$$, but as I said they wouldn't tell us how they calculated that.
I have posted this question on a couple of other sites as it's still sat in the moderation queue on the first one we tried.

Thanks
 
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What was the complete problem you were given, exactly as stated?
 
Hi, the problem was literally "make $$x$$ the subject:" with a list of equations such as:

Q:$$y=x+3$$
A:$$x=y-3$$

Q:$$y=x$$x$$5$$
A:$$x=\frac{y}{5}$$
 
Hi Subliminal, welcome to MHB! ;)

Your working is all correct.
If desired, we can substitute $y=1.2$ to find the corresponding value for $x$.
 
Hi, thanks for confirming this for me. Now to ask our lecturer point blank to explain their workings. Any tips on how to do this respectfully? ha, just joking.

I like Serena said:
Hi Subliminal, welcome to MHB! ;)

Your working is all correct.
If desired, we can substitute $y=1.2$ to find the corresponding value for $x$.

Funnily enough I was here a few years ago https://mathhelpboards.com/basic-probability-statistics-23/joint-probability-independent-events-16280-post75844.html#post75844!

I'm not actually sure what you mean here, it's been a while since I've studied maths!

Thanks again.
 
Subliminal said:
Hi, thanks for confirming this for me. Now to ask our lecturer point blank to explain their workings. Any tips on how to do this respectfully? ha, just joking.

Funnily enough I was here a few years ago https://mathhelpboards.com/basic-probability-statistics-23/joint-probability-independent-events-16280-post75844.html#post75844!

I'm not actually sure what you mean here, it's been a while since I've studied maths!

Thanks again.

Ah, my mistake. I saw someone with 4 posts that joined in September.
I just assumed that it was a couple of days ago without actually looking at the year. (Blush)
 
It's no problem, I appreciate the hospitality here, it helps this forum stand out amongst the others!
 
Anyway, you found $\frac{y}{5}-3=x$.
This is 'just' a relation. We cannot solve it any further and find unique numbers to satisfy it.
However, for a given $y$ we can find the corresponding value of $x$ now.
 
Sorry, I'm still not following. With my working I've replaced $$x$$ with $$1.2$$, as per our lecturers solution and it does make sense, but I'm unable to figure how the equation was simplified to get it:

$$x=1.2$$

$$y=5\left(1.2+3\right)$$

$$y=21$$

$$\frac{21}{5}-3=1.2=x$$

So, I can see it's "right", I just don't see how to work it to get that result.

Edit: I'm just confusing myself now >.<
 
  • #10
Subliminal said:
Sorry, I'm still not following. With my working I've replaced $$x$$ with $$1.2$$, as per our lecturers solution and it does make sense, but I'm unable to figure how the equation was simplified to get it:

$$x=1.2$$

$$y=5\left(1.2+3\right)$$

$$y=21$$

$$\frac{21}{5}-3=1.2=x$$

So, I can see it's "right", I just don't see how to work it to get that result.

You already gave an arbitrary example with $x=2$ to verify the result.
Your lecturer picked a different example with $x=1.2$ to verify it.
Both are correct.
 
  • #11
Ok, so as we have to show our working, how would they have come to the conclusion that $$x=1.2$$?
Thanks
 
  • #12
Subliminal said:
Ok, so as we have to show our working, how would they have come to the conclusion that $$x=1.2$$?
Thanks

They didn't. They just picked $x=1.2$ arbitrarily as an example. Any other value would be fine as well.
 
  • #13
Oh, it just clicked...

The entire point here is that $$x$$ can be anything, it's the method we use to find $$x$$ that is being assessed.

Sorry, I appreciate your patience!
 

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