Question

How do you solve for a in `2a - b = ac + 3b`?

Answer 1

`a=(4b)/(2-c)`

Explanation:

`"collect terms in a on the left side of the equation"`
`"and all other terms on the right side"`

`"add b to both sides"`

`2acancel(-b)cancel(+b)=ac+3b+b`

`rArr2a=ac+4b`

`"subtract "ac" from both sides"`

`2a-ac=cancel(ac)cancel(-ac)+4b`

`rArr2a-ac=4b`

`"factor out the a on the left side"`

`rArra(2-c)=4b`

`"divide both sides by "(2-c)`

`(acancel((2-c)))/cancel(2-c)=(4b)/(2-c)`

`rArra=(4b)/(2-c)`