Question

10x-35+3ax=5ax-7a solve for "a" for which the equation is an identity.

Answer 1

10x-35+3ax=5ax-7a
10x-35=5ax-7a-3ax
10x-35=a(5x-7-3x)
(10x-35)/(5x-7-3x)=a


therefore a=(10x-35)/(5x-7-3x)

Answer 2

`a=(10x-35)/(2x-7)`

Explanation:

We have been given an equation
`10x-35+3ax=5ax-7a`. We are asked to solve the given equation for 'a'.

Switch sides:

`5ax-7a=10x-35+3ax`

`5ax-3ax-7a=10x-35+3ax-3ax`

`2ax-7a=10x-35`

Factor out a:

`a(2x-7)=10x-35`

Divide both sides by
`(2x-7)`:

`(a(2x-7))/((2x-7))=(10x-35)/((2x-7))`

`a=(10x-35)/(2x-7)`

Therefore, our required equation would be
`a=(10x-35)/(2x-7)`.