Question

In the following exercises, solve.

$\sqrt[3]{4x+5}-2=-5$

Short answer

The solution of the given equation is $x=-8$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$\sqrt[3]{4x+5}-2=-5$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}\sqrt[3]{4x+5}& =& -5+2\\ \sqrt[3]{4x+5}& =& -3\end{array}$

Take cube on both sides.

$\begin{array}{rcl}(\sqrt[3]{4x+5}{)}^3& =& (-3{)}^3\\ 4x+5& =& -27\\ 4x& =& -27-5\\ 4x& =& -32\end{array}$

Divide both sides by 4.

$\begin{array}{rcl}\frac{4x}{4}& =& \frac{-32}{4}\\ x& =& -8\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=-8$.