Making X The Subject

**JadeKiara** · November 27th 2009, 12:03 AM

How can I do these?

Make x the subject:

1. $y= 2x-5/3$
2. $y= /sqrt{4+2x}$
3. $y= 1/x^3+8$
4. $y= k+ax/k-ax$

Thanks in advance!

**mathaddict** · November 27th 2009, 12:10 AM

Originally Posted by JadeKiara

How can I do these?

Make x the subject:

1. $y= 2x-5/3$
2. $y= /sqrt 4+2x$
3. $y= 1/x^3+8$
4. $y= k+ax/k-ax$

Thanks in advance!

HI

the idea here is to throw everything so that x is the only term at one side .

(1) y=2x-5/3

Multiply the whole thing by 3 ie 3y=6x-5

6x=3y+5

x=(3y+5)/6

$y=\frac{1}{x^3}+8$

$y-8=\frac{1}{x^3}$

$<br /> x^3=\frac{1}{y-8}<br />$

$x=\frac{1}{(y-8)^{\frac{1}{3}}}$

Try out the rest .

**JadeKiara** · November 27th 2009, 12:14 AM

Do you realise that the equation was $y=2x-5/3$ ?

I'm sorry, I am new to LaTex, and it was supposed to be:
1. y=2x-5/3
2. y=/sqrt{4+2x}
3. y=1/{x^3+8}
4. y={k+ax}/{k-ax}

**Grandad** · November 27th 2009, 12:44 AM

Hello JadeKiara

Originally Posted by JadeKiara

Do you realise that the equation was $y=2x-5/3$ ?

I'm sorry, I am new to LaTex, and it was supposed to be:
1. y=2x-5/3
2. y=/sqrt{4+2x}
3. y=1/{x^3+8}
4. y={k+ax}/{k-ax}

mathaddict's answer to #1 was based on the equation $y = 2x -\frac53$ , and was correct.

However, #3 was (correctly) based on your first post. But, following your alteration, it should be:

$y = \frac{1}{x^3+8}$

$\Rightarrow x^3+8 = \frac{1}{y}$ (Do you understand that step?)

$\Rightarrow x^3 = \frac{1}{y}-8$

$\Rightarrow x = \sqrt[3]{\frac{1}{y}-8}$

which could be written instead as

$\Rightarrow x = \sqrt[3]{\frac{1-8y}{y}}$

For #2:

$y = \sqrt{4+2x}$

$\Rightarrow y^2 = 4+2x$

Can you complete it from here?

And #4 is a bit trickier:

$y = \frac{k+ax}{k-ax}$

$\Rightarrow y(k-ax)=k+ax$

$\Rightarrow ky-ayx=k+ax$

$\Rightarrow ky-k = ax+ayx$

$\Rightarrow k(y-1)=a(1+y)x$ (Do you see how I've factorised each side?)

$\Rightarrow x = \frac{k(y-1)}{a(1+y)}$

Grandad

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