Question

How do you solve for `x` in `2x+b=w`?

Answer 1

`x=1/2(w-b)`

Explanation:

`color(red)("Using first principles")`

`color(red)("Step 1")`
Have only the terms with `x` in them on the left of the =

Subtract `color(blue)(b)` from both sides

`color(brown)(2x+b" "=" "w" "->" "2x+bcolor(blue)(-b)" "=" "w color(blue)(-b))`

`2x+0=w-b`

`2x=w-b`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(red)("Step 2")`
Have only `x` on the left hand side of the =

Divide both sides by `color(blue)(2)`

`color(brown)(2/(color(blue)(2))xx x=color(blue)(1/2)(w-b)`

`1xx x=1/2(w-b)`

`x=1/2(w-b)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(red)("Comment")`

`1/2(w-b)` is the same as `w/2-b/2`