Question

How do you solve for b in `a = 2b`?

Answer 1

`b = 1/2a`

Explanation:

As long as you perform the same arithmetic operation on both sides of an equation (exception: other than attempting to divide by zero) the equation remains valid.

If `a = 2b`
then we can divide both sides by 2
`color(white)("XXXX")` `a/2 = (cancel(2)b)/(cancel(2))`
`a/2` can be written `1/2a` (personal preference allowed)
`color(white)("XXXX")` `1/2a = b`

Or, since an equality is reflexive:
`color(white)("XXXX")` `b = 1/2 a`