Q. 328 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt[3]{8x-5}=\sqrt[3]{3x+5}$

Step-by-Step Solution

Answer

The solution of the given equation is $x=2$.

Step 1. Given information.

The given equation is:

$\sqrt[3]{8x-5}=\sqrt[3]{3x+5}$

Step 2. Solve the equation.

Take cube on both sides.

$\begin{array}{rcl}(\sqrt[3]{8x-5}{)}^3& =& (\sqrt[3]{3x+5}{)}^3\\ 8x-5& =& 3x+5\\ 8x-3x& =& 5+5\\ 5x& =& 10\end{array}$

Divide both sides by 5.

$\begin{array}{rcl}\frac{5x}{5}& =& \frac{10}{5}\\ x& =& 2\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=2$.