# Math Help - [SOLVED] Rearranging.

1. ## [SOLVED] Rearranging.

I have been given this equation.

$\Pi_t=\gamma\Pi_t+(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)$

And told it can be rearranged to get this.

$\Pi_t=\Pi_{t-1}-\frac{\alpha(u_t-u_n)}{(1-\gamma)}$

I don't understand how they got this. It's off my lecture slides.

2. Originally Posted by el123
I have been given this equation.

$\Pi_t=\gamma\Pi_t+(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)$

And told it can be rearranged to get this.

$\Pi_t=\Pi_{t-1}-\frac{\alpha(u_t-u_n)}{(1-\gamma)}$

I don't understand how they got this. It's off my lecture slides.

HI

$\Pi_t=\gamma\Pi_t+(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)$

$\Pi_t-\gamma\Pi_t=(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)$

$(1-\gamma)(\Pi_t)=(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)$

$\Pi_t=\frac{(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)}{1-\gamma}$

so it becomes

$\Pi_t=\Pi_{t-1}-\frac{\alpha(u_t-u_n)}{(1-\gamma)}$

3. Ahhhh! Thanks i see where i was getting confused now . Cheers!