# How do you solve 4=7-sqrt(33x-2)?

Jan 14, 2017

$x = \frac{1}{3}$

#### Explanation:

Given:$\text{ } 4 = 7 - \sqrt{33 x - 2}$

Swap the 4 with the square root (sign changes)

$\sqrt{33 x - 2} = 7 - 4 \text{ "=" } 3$

Square both sides

$33 x - 2 = 9$

$33 x = 11$

Divide both sides by 33

$x = \frac{11}{33}$

$x = \frac{11 \div 11}{33 \div 11} = \frac{1}{3}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Check}}$

$4 = 7 - \sqrt{33 x - 2}$

consider the RHS only

$7 - \sqrt{33 \left(\frac{11}{33}\right) - 2}$

$7 - \sqrt{9}$

$4$

Thus LHS=RHS