Question

In the following exercises, solve.
$(8x+5{)}^{\frac{1}{3}}+2=-1$

Short answer

The solution of the given equation is $x=-4$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$(8x+5{)}^{\frac{1}{3}}+2=-1$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}(8x+5{)}^{\frac{1}{3}}& =& -1-2\\ (8x+5{)}^{\frac{1}{3}}& =& -3\end{array}$

Take cube on both sides.

$\begin{array}{rcl}8x+5& =& (-3{)}^3\\ 8x& =& -27-5\\ x& =& \frac{-32}{8}\\ x& =& -4\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=-4$.