How do I solve this to get a alone without an a on the other side?

Question

asked Jul 21, 2023 137k views

1 Answer

MichaelJCox · Answer 1 · 2023-07-25T19:23:05+0000

First, lets multiply both sides of the equation by 'a':

$\begin{gathered} a\cdot(g=(1+2a)/(a)) \\ \Rightarrow a\cdot g=(1+2a)/(a)\cdot a=1+2a \\ \Rightarrow ag=1+2a \end{gathered}$

Now we have to move all the terms that have the variable 'a' to the left side of the equation:

$\begin{gathered} ag=1+2a \\ \Rightarrow ag-2a=1 \end{gathered}$

Notice that now we have that 'a' is common factor on the left side, then we can factor it and get the following:

$\begin{gathered} ag-2a=1 \\ \Rightarrow a(g-2)=1 \\ \Rightarrow a=(1)/(g-2) \\ \end{gathered}$

therefore, a=1/(g-2)