Question

2ax-b=cx+d solve for x

Answer 1

We have to solve the following equation for the variable x:

$2ax-b=cx+d$

For doing so, we assume that the variables a, b, c and d behave as normal numbers, and we will move the terms with x to the left side, and those who doesn't have it, to the right.

$\begin{gathered} 2ax-b-cx=cx+d-cx \\ 2ax-cx-b=d \\ 2ax-cx-b+b=d+b \\ 2ax-cx=d+b \end{gathered}$

Now, we will factor the variable x, as we want to have just one expression with x, thus:

$(2a-c)x=d+b$

And lastly, we will divide both sides by 2a-c, and we obtain:

$x=\frac{d+b}{2a-c}$

Which is the asked expression for x.