Q. 308 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt[3]{9x-1}-1=-5$

Step-by-Step Solution

Answer

The solution of the given equation is $x=-7$.

Step 1. Given information.

The given equation is:

$\sqrt[3]{9x-1}-1=-5$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}\sqrt[3]{9x-1}& =& -5+1\\ \sqrt[3]{9x-1}& =& -4\end{array}$

Take cube on both sides.

$\begin{array}{rcl}(\sqrt[3]{9x-1}{)}^3& =& (-4{)}^3\\ 9x-1& =& -64\\ 9x& =& -64+1\\ 9x& =& -63\end{array}$

Divide both sides by 9.

$\begin{array}{rcl}\frac{9x}{9}& =& \frac{-63}{9}\\ x& =& -7\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=-7$.