Q. 327 - Intermediate Algebra

Question

In the following exercises, solve.

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

Step-by-Step Solution

Answer

The solution of the given equation is $x=1$.

Step 1. Given information.

The given equation is:

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

Step 2. Solve the equation.

Take cube on both sides.

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

Divide both sides by 4.

$\begin{array}{rcl}\frac{4x}{4}& =& \frac{4}{4}\\ x& =& 1\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=1$.