Question

How do you solve for x in `a(x + b) = x + 4`?

Answer 1

`x=(4-ab)/(a-1)`

Explanation:

Expand the left side:
`color(white)("XXX")ax+ab=x+4`
Subtract `x` from both sides
`color(white)("XXX")ax+ab-x=4`
Subtract `ab` from both sides
`color(white)("XXX")ax-x=4-ab`
Factor the `x` out of the left side
`color(white)("XXX")x(a-1)=4-ab`
Divide both sides by `(a-1)`
`color(white)("XXX")x=(4-ab)/(a-1)`