# What value of x makes (2x+17)^1/3=3 a true statement?

Apr 7, 2018

$x = 5$

#### Explanation:

${\left(2 x + 17\right)}^{\frac{1}{3}} = 3$

$2 x + 17 = {3}^{3}$

$2 x + 17 = 27$

$2 x = 10$, so $x = 5$

Apr 7, 2018

$x = 5$.

#### Explanation:

We are given that ${\left(2 x + 17\right)}^{\frac{1}{3}} = 3$. We cube both sides of the equation:

${\left(2 x + 17\right)}^{\frac{1}{3}} = 3$,
${\left({\left(2 x + 17\right)}^{\frac{1}{3}}\right)}^{3} = {3}^{3}$,
$2 x + 17 = 27$.

Now we solve for $x$.

$2 x + 17 = 27$,
$2 x = 10$,
$x = 5$.