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$$1 = x + 2\cdot x$$

How can I simplify this formula for $x$.

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Are you actually looking for the roots of $x^2+x-1$? If so, you could start reading this and you will be able to proudly solve it on your own. If not, apologies, I have no idea what you are asking then. –  1015 Apr 29 '13 at 19:53
    
What is $x(2)$? Is it a $x^2$ or something else? –  m0nhawk Apr 29 '13 at 19:54
    
it's x times 2 or x*2 or x(2) –  Ben Apr 29 '13 at 19:54
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Wait, if this is $1=x+2x=3x$, this is trivially $x=\frac{1}{3}$ (in the real or complex numbers). –  1015 Apr 29 '13 at 19:59
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5 star! period. will get +1 from me. –  Kaster Apr 29 '13 at 20:00

2 Answers 2

By equivalent transform of terms/equations: $$\begin{align} 1&=x+2x \\ 1&=1\cdot x+2\cdot x \\ 1&=(1+2)\cdot x \\ 1&=3\cdot x \\ 1/3&=x \end{align}$$ In the last step we have divided by $3$ both sides of the equations. In the previous steps we used the unit and distributive properties:
$1\cdot x=x$ and $(a+b)\cdot x=a\cdot x+b\cdot x$.

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$$1 = x + 2 \cdot x$$ This can be simplified to: $$1 = x + 2x$$ Remember that you can combine these terms by adding the coefficients (the numbers attached to the $x$'s). $$1 = 1x + 2x$$ $$1 = 3x$$ Now we have to isolate $x$. Divide both sides by 3. $$\frac{1}{3} = \frac{3x}{3}$$ $$\frac{1}{3} = x$$ I hope this post helped!

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