# How do you solve 9- root[ 3] { 3x - 5} = 7?

Jul 8, 2017

$x = \frac{13}{3} \mathmr{and} 4.333333333$

#### Explanation:

$9 - \sqrt[3]{3 x - 5} = 7$

$\therefore - \sqrt[3]{3 x - 5} = 7 - 9$

$\therefore - \sqrt[3]{3 x - 5} = - 2$

multiply both sides by$- 1$

$\therefore \sqrt[3]{3 x - 5} = 2$

cube both sides

$\therefore {\left(\sqrt[3]{3 x - 5}\right)}^{3} = {\left(2\right)}^{3}$

$\therefore \sqrt[3]{a} \cdot \sqrt[3]{a} \cdot \sqrt[3]{a} = a$

$\therefore 3 x - 5 = {2}^{3}$

$\therefore 3 x - 5 = 8$

$\therefore 3 x = 8 + 5$

$\therefore 3 x = 13$

:.color(blue)(x=13/3 or 4.333333333

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)(Check:

substitute color(blue)(x=4.333333333

$\therefore 9 - \sqrt[3]{3 \left(\textcolor{b l u e}{4.333333333}\right) - 5} = 7$

$\therefore 9 - \sqrt[3]{13 - 5} = 7$

$\therefore - \sqrt[3]{13 - 5} = 7 - 9$

$\therefore - \sqrt[3]{8} = - 2$

Multiply both sides by $- 1$

$\therefore \sqrt[3]{2 \cdot 2 \cdot 2} = 2$

$\therefore \sqrt[3]{2} \cdot \sqrt[3]{2} \cdot \sqrt[3]{2} = 2$

:.color(blue)(2=2