Q. 313 - Intermediate Algebra

Question

In the following exercises, solve.

$(12x-3{)}^{\frac{1}{4}}-5=-2$

Step-by-Step Solution

Answer

The solution of the given equation is $x=7$.

Step 1. Given information.

The given equation is:

$(12x-3{)}^{\frac{1}{4}}-5=-2$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}(12x-3{)}^{\frac{1}{4}}& =& -2+5\\ (12x-3{)}^{\frac{1}{4}}& =& 3\end{array}$

Take power 4 on both sides.

$\begin{array}{rcl}12x-3& =& (3{)}^4\\ 12x& =& 81+3\\ 12x& =& 84\\ x& =& \frac{84}{12}\\ x& =& 7\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=7$.