Q. 312 - Intermediate Algebra

Question

In the following exercises, solve.
$(12x-5{)}^{\frac{1}{3}}+8=3$

Step-by-Step Solution

Answer

The solution of the given equation is $x=-10$.

Step 1. Given information.

The given equation is:

$(12x-5{)}^{\frac{1}{3}}+8=3$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}(12x-5{)}^{\frac{1}{3}}& =& 3-8\\ (12x-5{)}^{\frac{1}{3}}& =& -5\end{array}$

Take cube on both sides.

$\begin{array}{rcl}12x-5& =& (-5{)}^3\\ 12x& =& -125+5\\ x& =& \frac{-120}{12}\\ x& =& -10\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=-10$.