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

Apr 24, 2017

$x = 3$

#### Explanation:

$\textcolor{b l u e}{\text{Isolate the root ""by subtracting 4 from both sides}}$

$7 - 4 = \sqrt{12 - x} \cancel{+ 4} \cancel{- 4}$

$\Rightarrow \sqrt{12 - x} = 3$

$\text{to 'undo' the root "color(blue)"square both sides}$

${\left(\sqrt{12 - x}\right)}^{2} = {3}^{2}$

$\Rightarrow 12 - x = 9$

$\text{subtract 12 from both sides}$

$\cancel{12} \cancel{- 12} - x = 9 - 12$

$\Rightarrow - x = - 3 \Rightarrow x = 3$

$\textcolor{b l u e}{\text{As a check}}$

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

$\text{right side } = \sqrt{12 - 3} + 4 = \sqrt{9} + 4 = 3 + 4 = 7$

$\Rightarrow x = 3 \text{ is the solution}$