Question

In the following exercises, solve.
$(6x+1{)}^{\frac{1}{2}}-3=4$

Short answer

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

Step-by-step solution

Step 1. Given information.

The given equation is:

$(6x+1{)}^{\frac{1}{2}}-3=4$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}(6x+1{)}^{\frac{1}{2}}& =& 4+3\\ (6x+1{)}^{\frac{1}{2}}& =& 7\end{array}$

Take square on both sides.

$\begin{array}{rcl}6x+1& =& (7{)}^2\\ 6x& =& 49-1\\ x& =& \frac{48}{6}\\ x& =& 8\end{array}$

Step 3. Conclusion.

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