# Solving equation in terms of $x$

$x + .08x + (x +.08x).1 = 12$

I need to come up with a formula that solves for x. In a generic way that doesn't combine values of $x$.

For example: starting with $x + .08x = 12$

$$x = \frac{12}{1+ \frac{8}{100}}$$

I am using this for a php script for tax purposes and I know the equation is right, but I am having a hard time solving it generically for $x$. (It has been awhile since I have done algebra)

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Okay, we have $$x + .08x + .1(x + .08x) = 1.08x + .1(1.08x) = 1.1 \cdot 1.08x = 1.188x$$ Therefore, we must solve $$1.188x = 12 \implies x = \frac{12}{1.188} = \frac{1000}{99} = 10.\overline{10}$$
I got the answer to be 10.101 (using Wolfram Alpha), I will try to use your formula to calculate it –  Chris Muench Nov 27 '13 at 23:36