Q. 310 - Intermediate Algebra

Question

In the following exercises, solve.
$(3x-2{)}^{\frac{1}{2}}+1=6$

Step-by-Step Solution

Answer

The solution of the given equation is $x=9$.

Step 1. Given information.

The given equation is:

$(3x-2{)}^{\frac{1}{2}}+1=6$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}(3x-2{)}^{\frac{1}{2}}& =& 6-1\\ (3x-2{)}^{\frac{1}{2}}& =& 5\end{array}$

Take square on both sides.

$\begin{array}{rcl}3x-2& =& (5{)}^2\\ 3x& =& 25+2\\ x& =& \frac{27}{3}\\ x& =& 9\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=9$.