So I'm doing economics and it's been a good 10 years since I've done any algebra. I'm having difficulty rearranging equations. In the picture it shows the equation moving from:
ΔY = MPC x (ΔY-ΔT)
to
(1-MPC) x ΔY = -MPC x ΔT
to the "Final result" in the picture. I'm unsure of the steps involved to get there. I've watched many videos and googled a lot but I still can't wrap my head around it. Could someone please take me through the steps on how we arrive at the final result?
NOTE: MPC, ΔY etc are single values, not separate characters ie M, P and C
Your original equation is $$\Delta Y=MPC(\Delta Y-\Delta T)$$ Using the distributive property, you can expand the right-hand side, leading to the following result:$$\Delta Y=MPC\times\Delta Y-MPC\times\Delta T$$ Grouping all the terms that contain $\Delta Y$ gives $$\Delta Y-MPC\times\Delta Y=-MPC\times\Delta T$$ Since $\Delta Y$ is a common factor on the left-hand side, you can factorize it out as follows: $$\Delta Y(1-MPC)=-MPC\times\Delta T$$ Since you want to make $\Delta Y$ the subject of the formula, you can divide through by $(1-MPC)$ to obtain $$\Delta Y=\frac{-MPC}{1-MPC}\times\Delta T$$ and that is your answer. I hope it helps.