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Math Help - Making X The Subject

  1. #1
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    Making X The Subject

    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!
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  2. #2
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    Quote Originally Posted by JadeKiara View Post
    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 .
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  3. #3
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    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}
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  4. #4
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    Hello JadeKiara
    Quote Originally Posted by JadeKiara View Post
    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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