How to solve this problem? (Find the value of k in 4k² + 4m = 3m + n)

[RandomGuyThatNoobOnMath]

Plss help to to solve this problem

Find the value of k
4k² + 4m = 3m + n

I had tried to do like this
8k + 4m = 3m + n
8k + 4 = 3 + n
8k = –1 + n
k = –1 + n ÷ 8
k = –1 + n / 8
But the answer is wrong when I check
Can someone teach me how to do this ?
Please help??????

 

[JeffM]

What happened to m?

If $4k^2 + 4m = 3m + n$ and $m = 1$, then indeed it is true that
$4k^2 + 4m = 3m + n \implies 4k^2 + 4 = 3 + n$, but that is not true if m equals any other number.
But all you know is that m is A number, not that it is 1 specifically. So there is error # 1. How do you fix it?

Do you understand what exponents mean? Exponents are numbers in small type adjacent to a numeral or pronumeral on on its right. For example, $3^4$, the 4 is an exponent and $3^4 = 1 * 3 * 3 * 3 * 3.$

When you imply $4k^2 = 8k$, that is NOT generally true. The only number for which it is true is 2:
$4 * 2^2 = 4 * (1 * 2 * 2) = 16 = 8 * 2.$ But all you know is that k is A number, not that it is 2 specifically. So there is error # 2. How do you fix it?

 

[Harry_the_cat]

Can you please state the entire question? I'm not sure what you have written is correct??

 

[Mr. Bland]

The problem as stated:

$4k^2 + 4m = 3m + n$​

Your first step was to eliminate $m$:

$8k + 4 = 3 + n$​

(EDIT: I see on review that your first step was actually to transform $4k^2$ into $8k$. This is not correct in the general case because the operation involving $2$ is not multiplication, but exponentiation.)

Sometimes this can be achieved through division, but because there are other terms on both sides of the equation, dividing by $m$ will actually give this:

$\frac{4k^2}{m}+4=3+\frac{n}{m}$​

Consequently, the remaining steps don't work out because the first one is incorrect.

You want to solve for $k$, so your steps should work towards isolating $k$ on one side of the equation. I'd suggest your first step is to subtract $4m$:

$4k^2=3m + n - 4m$
$4k^2 = n - m$​

 

[Otis]

I find it interesting that @RandomGuyThatNoobOnMath incorrectly treats the exponent 2 as a factor in this thread, while @xⁿ + yⁿ = zⁿ ? incorrectly writes the factor 2 as an exponent in this post. ?
$\;$

 

[The Highlander]

I find it interesting that @RandomGuyThatNoobOnMath incorrectly treats the exponent 2 as a factor in this thread, while @xⁿ + yⁿ = zⁿ ? incorrectly writes the factor 2 as an exponent in this post. ?
$\;$

You still think they're the same person? ?
Clearly, neither has any clue how to handle Algebra! ?
Maybe it's a case of Jekyll & Hyde (or Hyde & Hyde) or perhaps the poor individual is just suffering from schizophrenia. ?
In any case, you should give up worrying about it, you need to devote all your spare time finding fault with me! ?

 

[stapel]

Plss help to to solve this problem

Find the value of k
4k² + 4m = 3m + n

I had tried to do like this
8k + 4m = 3m + n

How did the $\displaystyle 4k^2$ become $\displaystyle 8k$?

8k + 4 = 3 + n

Where did the variable $\displaystyle m$ disappear to?

8k = –1 + n
k = –1 + n ÷ 8

How did $\displaystyle 8k=-1+n$ become $\displaystyle k=-1+\frac{n}{8}$?

k = –1 + n / 8
But the answer is wrong when I check
Can someone teach me how to do this ?

We really aren't set up here to provide days or weeks of classroom instruction. If you're needing lessons, try online, such as here.

Thank you!

Eliz.

 

[Steven G]

I will show you how to do this one since you seem to be having so much trouble with it.

4k² + 4m = 3m + n. What I underlined are called terms. Only one underlined term has a k in it. Bring all the non k terms to the right (of the equal sign). Keep in mind when you move a term across the equal sign you need to change their sign.
So 4k² + 4m = 3m + n becomes 4k² = 3m + n - 4m. Now we can combine 3m - 4m to get -1m or simply -m.
Now we have 4k² = n - m.

Things being multiplied are called factors. 4k² is made up of two factors, namely 4 and k². Since k² has a k in it, we want to solve for k² (and then k). Hence we need to get rid of the 4. When you move a factor across an equal sign, you need to move factors across the division line. That is, factors in the numerator move to the denominator and factors in the denominator get moved to the numerator.

Therefore 4k² = n - m becomes $\displaystyle k^2 = \dfrac{n-m}{4}$.

If you know what k² equals, how do you solve for k?

 

[Otis]

give up worrying … devote all your spare time finding fault with me

You told you that I'm worried? I enjoy many hobbies, so there cannot be time for only one!
$\;$