x=5-.5(5-.5x)
The text tells me the answer is 10/3 but I just get 10. I'm a fourth year business student and I can't get this, pretty embarrassing. It's part of a bigger managerial economics problem.
Thanks for your help.
$\displaystyle x=5-\frac{1}{2}(5-\frac{1}{2}x)$
$\displaystyle \Rightarrow x=5-(\frac{5}{2}-\frac{1}{4}x)$
$\displaystyle \Rightarrow x=5-\frac{5}{2}+\frac{1}{4}x\ \$ Distribute the $\displaystyle -1$ (I'm gonna guess this is where you made your mistake)
$\displaystyle \Rightarrow x=\frac{5}{2}+\frac{1}{4}x$
$\displaystyle \Rightarrow x-\frac{1}{4}x=\frac{5}{2}$
$\displaystyle \Rightarrow x(1-\frac{1}{4})=\frac{5}{2}$
$\displaystyle \Rightarrow \frac{3}{4}x=\frac{5}{2}$
$\displaystyle \Rightarrow x=\frac{5}{2}\cdot \frac{4}{3} = \frac{10}{3}$