Question

How do you solve `7=sqrt(12-x)+4` and identify any restrictions?

Answer 1

`x=3`

Explanation:

`color(blue)"Isolate the root ""by subtracting 4 from both sides"`

`7-4=sqrt(12-x)cancel(+4)cancel(-4)`

`rArrsqrt(12-x)=3`

`"to 'undo' the root "color(blue)"square both sides"`

`(sqrt(12-x))^2=3^2`

`rArr12-x=9`

`"subtract 12 from both sides"`

`cancel(12)cancel(-12)-x=9-12`

`rArr-x=-3rArrx=3`

`color(blue)"As a check"`

substitute this value into the right side of the equation and if equal to the left side then it is the solution.

`"right side "=sqrt(12-3)+4=sqrt9+4=3+4=7`

`rArrx=3" is the solution"`