Steps for solving $T= (\frac{xr}{1000} n) + \frac{xc}{100} $ for $x$ I have a problem, a correct solution and not nearly enough tools to get from one to the other.
I had this formula ...
$$T= (\frac{xr}{1000} n) + \frac{xc}{100} $$
... and I needed to get here ...
$$x = \frac{ 1000 * T }{10 c + n r }$$
... so eventually I cheated by means of Wolfram Alpha using ...
$$T=(((x*r)/1000)*n) + ((x*c)/100)$$ solve for $x$.
How "should" I have got there? I will continue to try and get there on my own - but a "right" way would be really useful for me to be able to see and study. I'm not after a full algebra lesson or anything - just a clever human's steps maybe.
Sorry if this type of question isn't preferred here (?) - but if anyone wants to show how they would have done it I would greatly appreciate your time :)
Update: I can't believe that after just a few minutes I got not only a sensible correction to the question title but so much help.
I'm choosing the answer that helped my brain to engage the quickest and gave me the starting point I needed. Thank you all - moved by the help. Off to study.
UPDATE 2: The Internet. Wolfram Alpha. StackExchange. What a time to be alive.
 A: Can you get from
$$ 7 = (\frac{11x}{1000} \cdot 13) + \frac{17x}{100} $$
to $ x = \frac{7000}{170 + 11 \cdot 13} $ ?
A: I think you might be making this more complicated than it needs to be.
$$T= \left(\frac{xr}{1000} n\right) + \frac{xc}{100} = x\left(\frac{nr}{1000} + \frac{c}{100}\right),$$
which means that $$x = \frac{T}{\frac{nr}{1000} + \frac{c}{100}}.$$  Now, you can make this look nicer by finding a common denominator for the two fractions in the denominator:
$$x = \frac{T}{\frac{nr + 10c}{1000}} = \frac{1000T}{nr+10c}.$$
A: On problems like this, it's usually easiest if you can get rid of the fractions first. The least common multiple of 1000 and 100 is 1000, so we start by multiplying both sides by that:
$$ T = \frac{xr}{1000}n+\frac{xc}{100} $$
$$ 1000*T = 1000*\left[\frac{xr}{1000}n+\frac{xc}{100}\right] $$
Then, we can distribute 1000 on the right-hand side:
$$ 1000T = 1000\frac{xr}{1000}n+1000\frac{xc}{100} $$
The 1000's in the first term cancel, and $\frac{1000}{100}$ in the second simplifies to 10:
$$ 1000T = xrn+10xc $$
Then, we need to isolate $x$, but there's a factor of $x$ in both terms on the right, so we need to factor it out first:
$$ 1000T = x(rn+10c) $$
To isolate $x$ now, we just need to divide both sides by $(rn+10c)$ (that factor will cancel on the right):
$$ \frac{1000T}{(rn+10c)} = \frac{x(rn+10c)}{(rn+10c)} $$
$$ \frac{1000T}{(rn+10c)} = x $$
