Question

Solve for x in terms of y. Please help!

Answer 1

\[y=\sqrt{\frac{ 4x-1 }{ x }}\]

Answer 2

Every new problem I look at seems to make less and less sense.

Answer 3

\(\large\color{black}{ \displaystyle y^2=\frac{4x-1}{x} }\)

\(\large\color{black}{ \displaystyle y^2=\frac{4x}{x}-\frac{1}{x} }\)

\(\large\color{black}{ \displaystyle y^2=4-\frac{1}{x} }\)

can you take it from there?

Answer 4

all they are asking you to do, is to isolate the x (without performing incorrect operations).

Answer 5

\[x=\frac{ -1 }{ y^2-4 }\]

Answer 6

yes, and if you want you can simplify that just a bit, to get:

\(\large\color{black}{ \displaystyle x=\frac{1}{4-y^2} }\)

Answer 7

Ah, thanks again

Answer 8

You are always welcome

Answer 9

There is another one that I will try on my own for now but I'll ask if I need help again

Answer 10

Ok:)

Answer 11

\[y=\frac{ 1 }{ x^2+2x }\]
\[x^2+2x=\frac{ 1 }{ y }\]

Answer 12

the second equation is the next step that you took?

Answer 13

Yes

Answer 14

Ok, you can subtract -1/y from both sides, and do the quadratic formula.

a=1
b=2
c=1/y

Answer 15

i mean c=-1/y

Answer 16

Ah, ok

Answer 17

ill try that

Answer 18

\(\large\color{black}{ \displaystyle x^2+2x\color{red}{-\frac{1}{y}}=\frac{1}{y}\color{red}{-\frac{1}{y}} }\)

\(\large\color{black}{ \displaystyle x^2+2x-\frac{1}{y}=0 }\)

Answer 19

go on... :)

Answer 20

\[x=\frac{ -2+/-\sqrt{4+\frac{ 4 }{ y }} }{ }\]

Answer 21

over 2

Answer 22

you can do a \(\pm\) sign in latex by \pm
(just a code advise)

and yes, so far correct

Answer 23

\[x=-2\pm \sqrt{4y+4}\]

Answer 24

over 2 again

Answer 25

i don't think I followed you this time.
How come your y came from denominator to numerator?

Answer 26

\(\large\color{black}{ \displaystyle x=\frac{-2\pm\sqrt{4-4(1)(-\frac{1}{y})}}{2} }\)

\(\large\color{black}{ \displaystyle x=\frac{-2\pm\sqrt{4+4(\frac{1}{y})}}{2} }\)

it should be like this

Answer 27

ah

Answer 28

it can be simplified ....

Answer 29

\(\large\color{black}{ \displaystyle x=\frac{-2\pm\sqrt{4+4(\frac{1}{y})}}{2} }\)

\(\large\color{black}{ \displaystyle x=\frac{-2\pm2\sqrt{1+(\frac{1}{y})}}{2} }\)

\(\large\color{black}{ \displaystyle x=-1\pm\sqrt{1+\frac{1}{y}} }\)

Answer 30

this is it, technically, although, if you feel like or need to you can rationalize the denominator

Answer 31

Don't think do

Answer 32

Thank you so much

Answer 33

*think so

Answer 34

yw