Solve $\displaystyle 2^x=14-2x$ simultaneously.

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- Jan 31st 2009, 11:54 PMrequal[SOLVED] Simultaneous equations
Solve $\displaystyle 2^x=14-2x$ simultaneously.

- Jan 31st 2009, 11:59 PMred_dog
A solution is $\displaystyle x=3$.

Let $\displaystyle f(x)=2^x, \ g(x)=14-2x$

$\displaystyle f(x)$ is strictly increasing, and $\displaystyle g(x)$ is strictly decreasing, so the solution is unique. - Feb 1st 2009, 12:02 AMJhevon
this is not really simultaneous equation problem. you need more than one equation for that.

note that on the right, if you make x too big (bigger than 7), you get a negative answer. the left side is always positive, so you want to try x values that are less than 7. there is one positive solution (meaning you would try integer values for x). trial and error can find it - Feb 1st 2009, 12:10 AMMoo