Making 'x' the subject of this equation

chickenlegs

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Jan 19, 2020
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Could anyone help me make 'x' the subject of the following pension/ income tax formula?

NI = y+x-0.2((y+0.75x)-PA)

x=???

Many thanks
 
First of all I'd try to gather the x terms together. Start expanding the brackets on the RHS, which will "release" x!
 
First of all I'd try to gather the x terms together. Start expanding the brackets on the RHS, which will "release" x!

Or, you might be able to see directly that

x + c(a + t*x + b)

is equivalent to

x + c*t*x + c(a + b)

To see how this works, just fully expand

x + c(a + t*x + b)
x + c*a + c*t*x + c*b
x + c*t*x + c*a +c*b
x + c*t*x + c*(a +b)

--

Then the next step is to write

x*(1 + c*t) + c(a + b)

Could you do this with your equation, and post back the result?
 
Thank you - I am confused by your suggestions unfortunately as I don't quite see where c, t, a and b fit in to my question, however, I have, in the meantime, managed to quiz a maths teacher that I know and we have solved 'x' as follows:

x = (NI-0.2PA-0.8y)/0.85 and if I enter values for NI, PA and y, it seems to give me the right value for x. Thank you for responding.
 
Thank you - I am confused by your suggestions unfortunately as I don't quite see where c, t, a and b fit in to my question, however, I have, in the meantime, managed to quiz a maths teacher that I know and we have solved 'x' as follows:

x = (NI-0.2PA-0.8y)/0.85 and if I enter values for NI, PA and y, it seems to give me the right value for x. Thank you for responding.

Glad you got someone else to help. I can verify that your answer is correct, it is equivalent to mine...

x = 4/17 * (5*NI - 4*y - PA)

With the variables I was trying to give you a general hint about how to solve this. It would have been better if I'd worked with your actual numbers! BTW I like your username :)
 
Thank you Cubist, you have been very helpful. I'm sorry that I didn't quite get the hint - mathematics is not a strong point for me. I haven't had to resolve or extract parts of 'complex' equations for at least 156 years! Hence the call for help.
I needed the equation to work out the value of my yearly, gross personal pension; really exciting, but important in understanding if I am likely to run out of money in my old age!
Thank you for the interest in my username - it's a very good description of me!
Chris
 
Thank you Cubist, you have been very helpful. I'm sorry that I didn't quite get the hint - mathematics is not a strong point for me. I haven't had to resolve or extract parts of 'complex' equations for at least 156 years! Hence the call for help.
I needed the equation to work out the value of my yearly, gross personal pension; really exciting, but important in understanding if I am likely to run out of money in my old age!
Thank you for the interest in my username - it's a very good description of me!
Chris

Good luck with the admin/ pension stuff. Sounds like very tedious work so I'm not surprised that you were after a quick answer. Feel free to say in your post what the situation is, and I'm sure I (or one of the other helpers) would give you a more direct answer.

(Your username reminded me of a tongue in cheek nickname my father-in-law had for my daughter. Now she's a bit older he has stopped using it!)
 
By the way, you might be interested in the the website "WolframAlpha" which can automatically solve problems like this (most of the time). You just have to be careful to use a single letter variable name like p for PA and n for NI. Just type "rearrange n = y+x-0.2((y+0.75x)-p) for x" into the box. Click here to see the output.
 
Well that's just incredible and I will try and remember the web site should I ever have the misfortune to have to work out income tax and pension equations! Thank you for highlighting it. Chris
 
… managed to quiz a maths teacher … we have solved 'x' …
Hello. Did the teacher explain the steps (eg: distributive property, collecting like-terms)? If not and you're interested, let us know.

By the way, in the original equation below, the grouping symbols shown in red are not needed; they don't change anything.

NI = y + x - 0.2((y + 0.75x) - PA)

Cheers ?
 
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